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W3spoint99
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W3spoint99Begginer
Asked: December 30, 2024In:
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Explain Fundamental Forces in Nature (Class 11 – Physics) – Notes

cbseclass 11forcesfundamentalnaturephysics
  1. Saralyn
    Saralyn Begginer

    Fundamental Forces The most beautiful phenomenon that can be seen in physics is that how universe is so disciplined and synced together. The force has kept the universe bind together. Forces have always played an important role in the human existence, but it is not realized by humans. Human beings cRead more

    Fundamental Forces

    The most beautiful phenomenon that can be seen in physics is that how universe is so disciplined and synced together. The force has kept the universe bind together. Forces have always played an important role in the human existence, but it is not realized by humans. Human beings constantly experience some force acting on them like gravitational force, etc.  There are some forces that naturally exist in the universe, they are known as Fundamental Forces. Let’s learn about them in some detail.

    Force

    Force is an interaction, either with contact or without contact. When there is no opposition given to the Force, It can result in changing the motion, shape, position, of a body. Whenever some interaction occurs between two objects, there is a certain force acting upon them. There are many types of Forces present, For instance, Applied Force, Gravitational Force, Frictional Force, Tension Force, etc.

    Fundamental Forces in nature

    These forces are so well-defined that they cover the macroscopic and microscopic forces present in nature. The forces learned or seen by humans in everyday life, from frictional force, pull, push, thrust, etc. are known as derived forces, and they are not considered the fundamental forces. The derived forces are actually derived from the fundamental forces in some way or the other. Some Fundamental Forces are,

    • Gravitational Force
    • Electromagnetic Force
    • Strong Nuclear Force
    • Weak Nuclear Force

    These above-mentioned forces are responsible for all the observations obtained in forces present in the nature.

    Gravitational Force

    This force exists by the virtue of the masses of any objects. Gravitational force is the mutual force of attraction between two masses. Attraction between any mass and Earth is called Gravity. Isaac Newton first gave the concept of gravity. Gravity is the most intuitive and the weakest force present in nature. The Irony is that Gravity actually holds the planet, Solar system, Entire Universe together, yet it is known to be the weakest force present in nature.

    The Force of Gravitation is given as,

    Formula for Gravitational Force,

    F1=F2=G\frac{M1.M2}{r^2}

    Where, F = Force of Gravitation

    M1, M2 = Masses 1 and 2

    r = Distance between the masses

    G = Gravitational Constant (6.67× 10-11m3kg-1s-2)

    Electromagnetic Force

    Charges when they are at rest exert a force at each other known as the Electric force of attraction/repulsion. Like charges repel each other while unlike charges attract each other. When charges start to move and become dynamic, they develop magnetic field lines around and have magnetic force, these two forces combined are known as Electromagnetic forces present in nature.

    Magnetic force produced by current (moving charge)

    Combining the above two forces which are always perpendicular to each other will give rise to Electromagnetic Force. The force is produced by massless bosons and photons present in the charges, Electromagnetic force exists in nature and is responsible for many derived forces we experience every day, for example, Friction Force, Normal Force, Elasticity, and so on.

    Strong Nuclear Force

    It is the force of attraction between Protons and Neutrons. The force is the same whether protons and protons are present or neutrons and neutrons are present or protons and neutrons are looked at. In short, a Strong nuclear force exists between all nucleons. In short Ranges, this Force is the strongest among all the forces. It is important to note that at a distance of 10-13 cm, this force vanishes.

    Weak Nuclear Force 

    This Force is seen In the β Decay of a nucleus. Scientist named Wolfgang Pauli First predicted a particle named Neutrino. The Neutrino is an uncharged Particle that is released along with the electron in the β Decay process. During β Decay, when Beta Particle is ejected from an Atom, it tends to accelerate away from the atom and some force is required to accelerate the particle known as Weak Nuclear Force. Weak Nuclear Force is stronger than gravitational force but weaker than a strong nuclear force. 

    Table to represent Range and Relative Strength of Different Forces:

    Forces Range Relative strength
    Gravitational Force ∞ 10-38
    Electromagnetic Force ∞ 10-2
    Strong nuclear force < 10-15m 1
    Weak nuclear Force < 10-18m 10-13

    Conceptual Questions

    Question 1: Which Fundamental Force is the strongest and weakest among the fundamental forces present in nature?

    Answer:

    The strongest force present in nature is the Strong Nuclear Force and the weakest force present in nature at atomic scale is Gravity.

    Question 2: Which of the following forces are Fundamental, and which are derived in nature?

    Weak Nuclear Force, Friction Force, Gravity, Elasticity, Electromagnetic Force, Push

    Answer:

    Fundamental Forces ⇢ Weak Nuclear Force, Gravity, Electromagnetic Force.

    Derived Force ⇢ Friction Force, Elasticity, Push.

    Question 3: A statement is being used now “Gravity is not a force” Throw light on this statement.

    Answer:

    Isaac Newton initially discovered Gravity and Gravitational Force. It was then stated that gravity is a Force. Later on, with the help of Theory of Relativity, Einstein stated that Gravity is actually not a force but a result of space-time orientation. It is a consequence of masses moving along a geodesic lines in space time.

    Question 4: If the masses of 2 objects are doubled and the space between them is also doubled. How will the gravitational Force between them change?

    Answer:

    Gravitational Force is given as,

    F_G=G\frac{M_1.M_2}{r^2}

    When, Mass 1 and Mass 2 is doubled, M1’=2M1, M2’=2M2

    Distance between the masses is doubled, r’= 2r

    New Gravitational Force Between them,

    F_G'=G\frac{M_1'.M_2'}{r'^2}=G\frac{2M_1.2M_2}{4r^2} \\=G\frac{M_1.M_2}{r^2}=F_G

    Hence, The new value of gravitational Force will be same as the old Gravitational Force.

    Question 5: What are Pseudo Forces? Give Examples.

    Answer:

    Pseudo Forces are also known as Inertial Force or Fictitious Force. These forces actually do not exist and are the apparent forces that are seen due to fact that they are defined from a non-inertial frame.

    Example: A man sees another man going in a car and realized that some force is acting on the man in the car. This type of force seen is real as it is seen from a non-accelerated or inertial frame. However, the man in the car if looks at the man standing would feel that some force is acted upon the man and he is going backwards, this force is pseudo force, Since this force is seen from a non-inertial frame or an accelerated frame.

    Question 6: Which two forces have infinite range?

    Answer:

    The two fundamental forces having infinite range are Gravitational force and Electromagnetic force.

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W3spoint99
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W3spoint99Begginer
Asked: December 28, 2024In:
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How is Physics related to Other Sciences?

how physics relates to other sciencesinterdisciplinary sciencephysicsphysics and astronomyphysics and astronomy relationphysics and biologyphysics and chemistryphysics applicationsphysics explainedphysics in geologyrole of physics in sciencesscience connectionsscience educationscience videoSTEM education
  1. Saralyn
    Saralyn Begginer

    The word science comes from a Latin verb, Scientia. All the natural phenomena in the universe are governed by a systematic understanding known as Science. Natural phenomena can be predicted, controlled, modified as well as eradicated using the concepts of Science. It can be considered to be a globalRead more

    The word science comes from a Latin verb, Scientia. All the natural phenomena in the universe are governed by a systematic understanding known as Science. Natural phenomena can be predicted, controlled, modified as well as eradicated using the concepts of Science. It can be considered to be a global human endeavor. Science is concerned with physical nature and its aspects. It includes imagination, experimentation, and deduction.  Knowledge about Science has been gained by humans through experiments, observations, and trials conducted on the surrounding objects. Therefore, it is both knowledge and a process. The systematic and organized knowledge collected through various sources has formed a large pool, which is so vast today that it has been divided into many branches and sub-sections :

    • Physical Science- The science about the study of inanimate natural objects is referred to as the physical sciences. It majorly includes the following branches:   
      • Physics
      • Chemistry
      • Geology
      • Geography etc
    • Biological Science- The scientific study of life is referred to as the biological sciences.
      • Botany- Concerned with the study of plants.
      • Zoology- Concerned with the study of animals.
      • Ornithology etc

    Scientific Method and Scientific Theory

    The scientific method is a way to gain knowledge in a systematic and organized way. The process in the scientific method involves creating conjectures (hypotheses), deriving predictions out of these, and then carrying out empirical observations to validate those formulated and stipulated conjectures. 

    The scientific method goes through the formation of a sequence of steps to reach from the knowledge pool to well-formulated derivations and formulae. It consists of the following crucial steps :

    1. Systematic Observations
    2. Controlled Experiments
    3. Qualitative and Quantitative reasoning
    4. Mathematical Modelings
    5. Prediction and verification of theories.
    6. Speculation or Prediction

    Physics and its scope

    Physics is the branch of science related to the study of basic laws of nature and their manifestations concerned with the different natural phenomena. It is also referred to as the “fundamental science” because it constrains all the other significant branches of the sciences. It can be considered to be the study of the physical world and matter along with its motion through space and time. It also pertains to the concepts of energy and force as well.

    Physics consist of two principal types of approaches :

    1. Unification- Different constraints are applied to all the phenomena occurring together as a collection of universal laws in different domains in the world. It is an attempt to unify various laws and combine to carry out an activity. It is based on trial and process. For instance, both electric and magnetic phenomena are governed by electromagnetic laws.
    2. Reduction- This approach is based on the principle of deriving the properties of complex systems from the interactions, dependencies, and properties of their constituent parts. It can be used to understand the working of complex systems. For instance, the temperature of a system is reduced to average kinetic.

    Scope of Physics

    The scope of physics spreads over both massive objects like the universe and its surroundings, as well as to negligibly small-sized particles, like electrons, protons, etc., It is vast as it converts quantities with varying lengths stretching over a magnitude as high as 1060 m (study of the universe) or as low as 10-12 m (study of electrons, protons, etc). It also encompasses a wide range of masses from minutely small, like protons, neutrons etc., 10-10 kg, to highly massive galaxies, 1080 kg. Physics considers both the microscopic and macroscopic domains.

    Physics is divided into two major categories based on its scope:

    1. Classical Physics: Deals with the macroscopic phenomena (mechanics, thermodynamics, and electromagnetism). It can be considered to be a sub-branch of applied mathematics. The laws of motion framed by Isaac Newton were designed and developed keeping in mind the principles of classical physics.
    2. Modern Physics: Deals with microscopic phenomena (Special Relativity, Quantum Mechanics).

    Some Branch of Physics

    1. Mechanics- The branch of physics dealing with the movement of physical objects, more specifically the relationships between force, matter, and motion associated between them. It takes into consideration the objects both at rest and in motion. 
    2. Electrodynamics- The branch of physics dealing with rapidly changing electric and magnetic fields. It also pertains to the understanding of the particle motion and interactions produced within the variable fields. Maxwell devised numerous laws that are concerned with the motion of electric fields and their attributes.  
    3. Optics- The branch of physics dealing with the behavior and the interactions of light with each other. It can be used to simulate the construction of devices used to visualize and detect the aspects and components of light. It takes into account both ray and wave optics. It involves concepts related to the formation of images and the working of topics of reflection, refraction as well as diffraction. 
    4. Thermodynamics- The branch of physics related to heat and energy and its involved concepts. It also described the relationship with radiation along with the physical properties of matter. It also includes the conversion of heat into different types of energy; mechanical or electrical energy.

    Physics in Relation to Other Sciences

    Physics is a very significant branch of science that plays a crucial role in understanding the developments pertaining to the other branches of science, such as Chemistry, Biology, etc.

    • Physics in relation to Mathematics. The study of physical variables involved in the study of mathematics has led to the discovery of ideas of differentiation, integration, and differential equations involved in the estimation of quantities. Theories in physics and derivations in mathematics coexist with each other. Math is considered to be a deterministic tool for the development of modern theoretical physics. It provides a way to formulate and evaluate experimental results.
    Mathematics  Physics
    Graph Represents a single object. Represents a relationship between two quantities.
    Axes Dimensionless numbers are represented by linear scaling Values of quantities are expressed in some units. Scaling may be linear or non-linear.
    Origin (0,0) Any arbitrary position.
    Plot range infinite The ranges of the quantities.
    Slope Gradient Dimensionless numbers have a geometric interpretation only. Change of one quantity with respect to another.
    • Physics in relation to Biology. Physics form the essence of the field of biology. The concepts and illustrations of space, time, and matter have induced a better understanding of the existence of living organisms and the study of the laws of conversation of energy. Many diseases and ailments have been better diagnosed over the years due to developments in physics and vice versa. Disease diagnosis has been very efficient due to X-ray invention and practices. 
    • Physics in relation to Chemistry. Chemistry is basically an extension of Physics. The concepts associated with X-ray diffraction and radioactivity have revolutionized the study of the periodic table. The intra-particle forces, as well as internal interactions, can also be used to get a better insight into the bonding and the chemical structure of substances. The structure, behavior, and properties of matter are both easily understood with both the branches existing together.
    • Physics in relation to Meteorology. Meteorology holds an explicit part in the discipline of physics. It tends to explain nature’s observed behavior through estimated hypotheses and conjectures while taking into consideration the various relativistic repercussions. Atmospheric physics and meteorology use both mathematical and physical models to understand the weather and climatic conditions. It also relates to the descriptive mathematical and computer modeling of atmospheric dynamics.   
    • Physics in relation to Astronomy. The branch of astronomy is considered to be applied physics since it applies the scientific hypotheses and basic rules of physics to further the understanding of the celestial bodies and universe.For instance, the discovery and usage of radio telescopes, as well as optical telescopes, have stipulated an easy way to explore the universe.
    Type of forces Governs 
    Gravitational force All objects in the universe
    Weak nuclear force Particularly electrons and neutrinos.
    Electromagnetic force Charged particles
    Strong nuclear force Nucleons, heavier elementary particles

    The other sciences, like geology, oceanology, seismology, etc, also use some laws of physics.

    Sample Problems

    Problem 1: What is “high-energy” physics? 

    Solution: 

    High-energy physics, which is also termed particle physics, refers to the study of the elementary constituents of matter and energy along with their corresponding interactions. Particle physics is concerned with the design and development of high-energy accelerators and detectors.

    Problem 2: Explain the relation of physics to seismology. 

    Solution: 

    Seismology is also referred to as the scientific study concerned with earthquakes and their related phenomena, such as volcanic eruptions. The movement of the earth’s crust, that is, the tectonic shifts and the types of waves emitting energy helps us in studying the earthquake and its repercussions.

    Problem 3: Differentiate between weak and strong nuclear forces. 

    Solution:

    The difference between weak and strong nuclear forces are as follows:

    Weak nuclear forces Strong nuclear forces
    It makes the radioactive particles decay. It keeps the protons and neutrons of a nucleus together.
    Weak and very short-ranged. Strong and short ranged.
    Example: Conversion of a proton to a neutron. Example: fusion process between stars and the sun.

    Problem 4: What is the difference between classical and modern physics? 

    Solution: 

    Classical physics deals with the study of objects on a macroscopic scale, which can be studied with the largely unaided five human senses. This is in comparison to modern physics, which is concerned with the nature and behavior of particles and energy at the sub-microscopic level. The laws of one branch of physics remain inapplicable to the other branch and vice versa. Also, most of the laws of classical physics are deterministic.

    Problem 5: Define astrophysics. 

    Solution: 

    Astrophysics is a branch of science dealing with the methods and principles deployed in the study of astronomical objects and phenomena of the universe.

    Problem 6: Explain the reasons behind the durability of scientific knowledge. 

    Solution: 

    • It is easily corroborated by multiple scientists working independently.
    • Consistent and accurate with different scientists.
    • Vast knowledge accumulating over many years.

    Problem 7: Is it possible to modify a scientific theory? 

    Solution: 

    A scientific theory can be revised if required to accommodate new phenomena or data. It is not fixed and can be reformulated.

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W3spoint99
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W3spoint99Begginer
Asked: December 28, 2024In:
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Explain Types Of Sets with Examples.

learn mathematicsmath sets tutorialnull setspower setsset theory basicssets in mathematicssingleton setstypes of setstypes of sets explained
  1. Saralyn
    Saralyn Begginer

    Sets are a well-defined collection of objects. Objects that a set contains are called the elements of the set. We can also consider sets as collections of elements that have a common feature. For example, the collection of even numbers is called the set of even numbers. Table of Content What is Set?Read more

    Sets are a well-defined collection of objects. Objects that a set contains are called the elements of the set. We can also consider sets as collections of elements that have a common feature. For example, the collection of even numbers is called the set of even numbers.

    Table of Content

    What is Set?

    A well-defined collection of Objects or items or data is known as a set. The objects or data are known as the element. For Example, the boys in a classroom can be put in one set, all integers from 1 to 100 can become one set, and all prime numbers can be called an Infinite set. The symbol used for sets is {…..}. Only the collection of data with specific characteristics is called a set.

    Example: Separate out the collections that can be placed in a set.

    • Beautiful Girls in a class
    • All even numbers
    • Good basketball players
    • Natural numbers divisible by 3
    • Number from 1 to 10

    Answer:

    Anything that tries to define a certain quality or characteristics can not be put in a set. Hence, from the above given Collection of data. 

    The ones that can be a set,

    • All even numbers
    • Natural numbers divisible by 3.
    • Number from 1 to 10

    The ones that cannot be a set,

    • Beautiful girls in the park
    • Good basketball players

    Types of Sets in Mathematics

    Sets are the collection of different elements belonging to the same category and there can be different types of sets seen. A set may have an infinite number of elements, may have no elements at all, may have some elements, may have just one element, and so on. Based on all these different ways, sets are classified into different types.

    The different types of sets are:

    Singleton Set

    Empty Set

    Finite Set

    Infinite Set

    Equal Set

    Equivalent Set

    Subset

    Power Set

    Universal Set 

    Disjoint Sets

    Let’s discuss these various types of sets in detail.

    Singleton Set

    Singleton Sets are those sets that have only 1 element present in them.

    Example: 

    • Set A= {1} is a singleton set as it has only one element, that is, 1.
    • Set P = {a : a is an even prime number} is a singleton set as it has only one element 2.

    Similarly, all the sets that contain only one element are known as Singleton sets.

    Empty Set

    Empty sets are also known as Null sets or Void sets. They are the sets with no element/elements in them. They are denoted as ϕ.

    Example:

    • Set A= {a: a is a number greater than 5 and less than 3}
    • Set B= {p: p are the students studying in class 7 and class 8}

    Finite Set

    Finite Sets are those which have a finite number of elements present, no matter how much they’re increasing number, as long as they are finite in nature, They will be called a Finite set.

    Example: 

    • Set A= {a: a is the whole number less than 20}
    • Set B = {a, b, c, d, e}

    Infinite Set

    Infinite Sets are those that have an infinite number of elements present, cases in which the number of elements is hard to determine are known as infinite sets. 

    Example: 

    • Set A= {a: a is an odd number}
    • Set B = {2,4,6,8,10,12,14,…..}

    Equal Set

    Two sets having the same elements and an equal number of elements are called equal sets. The elements in the set may be rearranged, or they may be repeated, but they will still be equal sets.

    Example:

    • Set A = {1, 2, 6, 5}
    • Set B = {2, 1, 5, 6}

    In the above example, the elements are 1, 2, 5, 6. Therefore, A= B.

    Equivalent Set

    Equivalent Sets are those which have the same number of elements present in them. It is important to note that the elements may be different in both sets but the number of elements present is equal. For Instance, if a set has 6 elements in it, and the other set also has 6 elements present, they are equivalent sets.

    Example:

    Set A= {2, 3, 5, 7, 11}

    Set B = {p, q, r, s, t}

    Set A and Set B both have 5 elements hence, both are equivalent sets.

    Subset

    Set A will be called the Subset of Set B if all the elements present in Set A already belong to Set B. The symbol used for the subset is ⊆

    If A is a Subset of B, It will be written as A ⊆ B

    Example:

    Set A= {33, 66, 99}

    Set B = {22, 11, 33, 99, 66}

    Then, Set A ⊆ Set B 

    Power Set

    Power set of any set A is defined as the set containing all the subsets of set A. It is denoted by the symbol P(A) and read as Power set of A.

    For any set A containing n elements, the total number of subsets formed is 2n. Thus, the power set of A, P(A) has 2n elements.

    Example: For any set A = {a,b,c}, the power set of A is?

    Solution:

    Power Set P(A) is,

    P(A) = {ϕ, {a}, {b}, {c}, {a, b}, {b, c}, {c, a}, {a, b, c}}

    Universal Set 

    A universal set is a set that contains all the elements of the rest of the sets. It can be said that all the sets are the subsets of Universal sets. The universal set is denoted as U.

    Example: For Set A = {a, b, c, d} and Set B = {1,2} find the universal set containing both sets.

    Solution:

    Universal Set U is,

    U = {a, b, c, d, e, 1, 2}

    Disjoint Sets

    For any two sets A and B which do have no common elements are called Disjoint Sets. The intersection of the Disjoint set is ϕ, now for set A and set B A∩B =  ϕ. 

    Example: Check whether Set A ={a, b, c, d} and Set B= {1,2} are disjoint or not.

    Solution:

    Set A ={a, b, c, d}
    Set B= {1,2}

    Here, A∩B =  ϕ

    Thus, Set A and Set B are disjoint sets.

    Also, Check

    Summarizing Types of Set

    There are different types of sets categorized on various parameters. Some types of sets are mentioned below:

    Set Name Description Example
    Empty Set A set containing no elements whatsoever. {}
    Singleton Set A set containing exactly one element. {1}
    Finite Set A set with a limited, countable number of elements. {apple, banana, orange}
    Infinite Set A set with an uncountable number of elements. {natural numbers (1, 2, 3, …)}
    Equivalent Sets Sets that have the same number of elements and their elements can be paired one-to-one. Set A = {1, 2, 3} and Set B = {a, b, c} (assuming a corresponds to 1, b to 2, and c to 3)
    Equal Sets Sets that contain exactly the same elements. Set A = {1, 2} and Set B = {1, 2}
    Universal Set A set containing all elements relevant to a specific discussion. The set of all students in a school (when discussing student grades)
    Unequal Sets Sets that do not have all the same elements. Set A = {1, 2, 3} and Set B = {a, b}
    Power Set The set contains all possible subsets of a given set. Power Set of {a, b} = { {}, {a}, {b}, {a, b} }
    Overlapping Sets Sets that share at least one common element. Set A = {1, 2, 3} and Set B = {2, 4, 5}
    Disjoint Sets Sets that have no elements in common. Set A = {1, 2, 3} and Set B = {a, b, c}
    Subset A set where all elements are also members of another set. {1, 2} is a subset of {1, 2, 3}

    Solved Examples on Types of Sets

    Example 1: Represent a universal set on a Venn Diagram.

    Solution:

    Universal Sets are those that contain all the sets in it. In the below given Venn diagram, Set A and B are given as examples for better understanding of Venn Diagram.

    Example:

    Set A= {1,2,3,4,5}, Set B = {1,2, 5, 0}

    U= {0, 1, 2, 3, 4, 5, 6, 7}

    Universal Set

    Example 2: Which of the given below sets are equal and which are equivalent in nature?

    • Set A= {2, 4, 6, 8, 10}
    • Set B= {a, b, c, d, e}
    • Set C= {c: c ∈ N, c is an even number, c ≤ 10}
    • Set D = {1, 2, 5, 10}
    • Set E= {x, y, z}

    Solution:

    Equivalent sets are those which have the equal number of elements, whereas, Equal sets are those which have the equal number of elements present as well as the elements are same in the set.

    Equivalent Sets = Set A, Set B, Set C.

    Equal Sets = Set A, Set C.

    Example 3: Determine the types of the below-given sets,

    •  Set A= {a: a is the number divisible by 10}
    • Set B = {2, 4, 6}
    • Set C = {p}
    • Set D= {n, m, o, p}
    • Set E= ϕ

    Solution:

    From the knowledge gained above in the article, the above-mentioned sets can easily be identified.

    • Set A is an Infinite set.
    • Set B is a Finite set
    • Set C is a singleton set
    • Set D is a Finite set
    • Set E is a Null set

    Example 4: Explain which of the following sets are subsets of Set P,

    Set P = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

    • Set A = {a, 1, 0, 2}
    • Set B ={0, 2, 4}
    • Set C = {1, 4, 6, 10}
    • Set D = {2, 20}
    • Set E ={18, 16, 2, 10}

    Solution:

    • Set A has elements a, 1, which are not present in the Set P. Therefore, set A is not a Subset.
    • Set B has elements which are present in set P, Therefore, Set B ⊆ Set P
    • Set C has 1 as an extra element. Hence, not a subset of P
    • Set D has 2, 20 as element. Therefore, Set D ⊆ Set P
    • Set E has all its elements matching the elements of set P. Hence, Set E ⊆ Set P.

    FAQs on Types of Sets

    What are sets?

    Sets are well-defined collections of objects. 

    Example: The collection of Tata cars in the parking lot is a set.

    What are Sub Sets?

    Subsets of any set are defined as sets that contain some elements of the given set. For example, If set A contains some elements of set B set A is called the subset of set B.

    How many types of sets are present?

    Different types of sets used in mathematics are 

    • Empty Set
    • Non-Empty Set
    • Finite Set
    • Infinite Set
    • Singleton Set
    • Equivalent Set
    • Subset
    • Superset
    • Power Set
    • Universal Set

    What is the difference between, ϕ and {ϕ}?

    The difference between ϕ and {ϕ} is

    • ϕ = this symbol is used to represent the null set, therefore, when only this symbol is given, the set is a Null set or empty set.
    • {ϕ}= In this case, the symbol is present inside the brackets used to denote a set, and therefore, now the symbol is acting like an element. Hence, this is a Singleton set.
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