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The Reason is laravel is treating both as same, for example if you send a request http://127.0.0.1:8000/items/approved http://127.0.0.1:8000/items/1232 Technically it should work as expected but due to laravel wildcard it look for but Laravel interprets ...
How is Physics related to Other Sciences?
Explain Types Of Sets with Examples.
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
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.
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
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:
|
Equivalent Set |
|
Let’s discuss these various types of sets in detail.
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 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 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 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,…..}
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 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.
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 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}}
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}
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
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} |
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}
Example 2: Which of the given below sets are equal and which are equivalent in nature?
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,
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}
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.
Sets are well-defined collections of objects.
Example: The collection of Tata cars in the parking lot is a set.
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.
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
See lessThe 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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Explain – Representation of a Set (Class 11 – Maths). Please also Provide Some examples.
Imagine a very haphazard world where no categories are divided to memorize and classify things separately, a world like this will be full of chaos and mess, this is why humans prefer to categorize things and classify them to neatly understand and remember them. The same case happens in mathematics,Read more
Imagine a very haphazard world where no categories are divided to memorize and classify things separately, a world like this will be full of chaos and mess, this is why humans prefer to categorize things and classify them to neatly understand and remember them. The same case happens in mathematics, studying math involves dealing with a lot of data, and when the data can be grouped, it is preferred to group them and categorize them, hence, Sets come into play.
Sets are defined as the collection of well-defined data. In Math, a Set is a tool that helps to classify and collect data belonging to the same category, even though the elements used in sets are all different from each other, they all are similar as they belong to one group. For instance, a set of different outdoor games, say set A= {Football, basketball, volleyball, cricket, badminton} all the games mentioned are different, but they all are similar in one way as they belong to the same group (outdoor games).
The set is denoted as a capital letter, for example, set A, set B, etc., and the elements belonging to the set are denoted as a small letter, and they are kept in curly brackets {}, for example, set A= {a, b, c, d}, as it is clear that a, b, c, d belong to set A, it can be written a ∈ A, do p belong to set A? No. Therefore, it will be written as, p∉ A.
Sets can be represented in two ways, one is known as the Roster form and the other is famous as the Set-Builder form, these two forms can be used to represent the same data, but the style varies in both cases.
In Roster Form, the elements are inside {}⇢ Curly brackets. All the elements are mentioned inside and are separated by commas. Roster form is the easiest way to represent the data in groups. For example, the set for the table of 5 will be, A= {5, 10, 15, 20, 25, 30, 35…..}.
- The arrangement in the Roster form does not necessarily to be in the same order every time. For example, A= {a, b, c, d, e} is equal to A= {e, d, a, c, b}.
- The elements are not repeated in the set in Roster form, for example, the word “apple” will be written as, A= {a, p, l, e}
- The Finite sets are represented either with all the elements or if the elements are too much, they are represented as dots in the middle. The infinite sets are represented with dots in the end.
In Set-builder form, elements are shown or represented in statements expressing relations among elements. The standard form for Set-builder, A= {a: statement}. For example, A = {x: x = a3, a ∈ N, a < 9}
- In order to write the set in Set- builder form, the data should follow a certain pattern.
- Colons (:) are necessary in Set-builder form.
- After colon, the statement is to be written.
The order of the Set is determined by the number of elements present in the Set. For example, if there are 10 elements in the set, the order of the set becomes 10. For finite sets, the order of the set is finite, and for infinite sets, the order of the set is infinite.
Question 1: Determine which of the following are considered assetsin and which are not.
Answer:
Sets are not those bunches or groups where some quality or characteristic comes in the picture. Therefore,
- “All even numbers on the number line” is a set.
- “All the good basketball players from class 9th” is not a Set as “good” is a quality which is involved.
- “The bad performers from the batch of dancers” cannot be a Set since “bad” is a characteristic.
- “All prime numbers from 1 to 100” is a Set.
- “Numbers that are greater than 5 and less than 15” is a Set.
Question 2: Represent the following information inSet-Builder the Roster form.
Answer:
The Roster form for the above information,
- Set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11……}
- Set B = {} ⇢ Null set, since there are no numbers greater than 6 and less than 3.
- Set C = {10, 12, 14, 16, 18, 20, 22, 24}
Question 3: Express the given information in the Set-Builder form.
Answer:
The Set-Builder form for the above information,
- A = {a: a∈ N and 10 < a < 20}
- B = {b: b∈ N and b > 25}
- C = {c: c is the vowel of English Alphabet}
Question 4: Convert the following Sets given in Roster form into Set-Builder form.
Answer:
The Set- builder form for the above Sets,
- A = {a: a is a consonant of the English Alphabet}
- B = {b: b is an Even number and 2 ≤ b ≤10}
- C = {c: c is an odd number and 5 ≤ c ≤ 19}
Question 5: Give an example of the following types of Sets in both Roster form and Set-builder form.
Solution:
The Examples can be taken as per choice since there can be a infinite number of examples for any of the above Sets,
- Singular Set
Roster Form: A = {2}
Set- builder form: A= {a: a∈N and 1<a<3}
- Finite Set
Roster Form: B = {0,1, 2, 3, 4, 5}
Set-builder form: B = {b: b is a whole number and b<6}
- Infinite Set
Roster Form: C = {2, 4, 6, 8, 10, 12, 14, 16…..}
Set- builder form: C= {c: c is a Natural and Even number}
Question 6: What is the order of the given sets,
Answer:
The order of the set tells the number of element present in the Set.
- The order of Set A is 5 as it has 5 elements.
- The order of set B is 26 as the English Alphabet have 26 letters.
- The order of set C is infinite as the set has the infinite number of elements.
Question 7: Express the given Sets in Roster form,
Answer:
See lessRepresenting the above Set-builder sets in Roster form,
- A = {1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2}
- B = {1, 4, 9, 16, 25}
Explain – Biological Classification (NCERT Class 11 Chapter 2 Biological Classification).
Notes for NCERT Class 11 Chapter 2 Biological Classification: Biological classification is the process by which biologists group living organisms which, are classified on the basis of their similarity. Classification is essential for the convenient study of living organisms. It is required to identiRead more
Notes for NCERT Class 11 Chapter 2 Biological Classification: Biological classification is the process by which biologists group living organisms which, are classified on the basis of their similarity. Classification is essential for the convenient study of living organisms. It is required to identify different varieties of organisms. It helps in the correct identification of many organisms. It leads to the evolution of organisms. It also establishes phylogenetic relationships among organisms. Carolus Linneuas was one of the scientists to classify organisms.
NCERT Class 11 Biology Chapter 02 Biological Classification: The practice of classifying organisms based on shared characteristics is known as biological classification. Linnaeus proposed two areas of classification. He divided organisms into two kingdoms: the animal kingdom (Animalia) and the plant kingdom (Plantae). The classification of the two kingdoms had some disadvantages, such as the impossibility of distinguishing between eukaryotes and prokaryotes, unicellular and multicellular species, and photosynthetic and non-photosynthetic organisms. As a result, the field continued to grow and served as a primary example of R.H. Whittaker’s classification of the five domains or kingdoms.
Two kingdom classification was given by a biologist, Carolus Linnaeus. He classified organisms into two kingdoms, i.e. Plantae (included all plants) and Animalia (included all animals).
This system didn’t distinguish between the following types of organisms-
In 1969, R.H. Whittaker proposed the five-kingdom classification. He classified those five kingdoms as Monera, Protista, Fungi, Plantae, and Animalia. He primarily used the following criteria for classification:
Bacteria are the main members of this kingdom. Kingdom Monera is further divided into:
They are special bacteria as they can withstand extreme environmental conditions because of their different cell wall structure. They can be:
They have rigid cell walls and flagellum (locomotion), if motile. They can be photosynthetic autotrophs, chemosynthetic autotrophs and heterotrophs.
Heterocyst
They reproduce by asexual mode- binary fission, sexual mode- transfer of DNA and spore formation in unfavourable conditions.
They are the smallest organisms which lack cell walls. They can survive in the absence of oxygen (anaerobic). They cause diseases (pathogens).
They are single-celled eukaryotes. They include:
| Classification of Protista | Characteristic Features | Examples |
| Chrysophytes (chief producers in oceans) | Their cell walls form two overlapping shells, which are fit together and embedded with silica which, makes them indestructible. So, cell wall deposits and their accumulation leads to ‘diatomaceous earth’. This soil can be used to polish things, and filter oils and syrups. | Diatoms and golden algae (desmids) |
| Dinoflagellates | They show rapid multiplication and make the appearance of sea red (bioluminescence). Toxins released by them can kill other aquatic animals. | Red dinoflagellates (Example: Gonyaulax) |
| Euglenoids | They have a pellicle protein-rich layer) which keeps them flexible | Euglena |
| Slime Moulds | During suitable conditions, they form plasmodium and during unfavourable conditions, plasmodium differentiates and forms fruiting bodies (spores inside) |
Acrasia, Plasmodiophorina |
| Protozoans | They are heterotrophs and live as predators or parasites. They are classified into four types | Plasmodium |
| Protozoans | Features/Diseases Caused | Examples |
| Amoeboid Protozoans | They form pseudopodia to capture their prey. Some of them are parasites | Amoeba, Entamoeba |
| Flagellated Protozoans | Sleeping sickness, a disease caused by the parasitic forms | Trypanosoma |
| Ciliated Protozoans | Cilia (locomotion) and gullet, a cavity is present on the body | Paramoecium |
| Sporozoans | Some species cause malaria | Plasmodium |
Fungi are multicellular and the how heterotrophic mode of nutrition (saprophytes/parasites/symbiotic- mycorrhiza). Some fungi are unicellular, e.g. yeast.
Mushrooms and yeast are the most valuable fungi. Mushrooms are edible and are a good source of proteins. Yeast is used to make bread and cheese. Penicillium fungi are used to produce antibiotics.
Some fungi cause diseases in both plants and animals, e.g. wheat rust disease is caused by Puccinia fungus.
There are three modes of reproduction in fungi, i.e. vegetative, asexual and sexual.
In ascomycetes and basidiomycetes, the dikaryotic stage (n + n, i.e., two nuclei per cell) is formed, known as dikaryon and the phase is dikaryophase.
| Classification of Fungi | Characteristic Features | Examples |
| Phycomycetes | They grow on decaying wood in moist sites and obligate parasites on plant bodies | Mucor, Rhizopus (bread mould fungi) and Albugo (parasitic fungi on mustard) |
| Ascomycetes (sac-fungi) | Neurospora is used in biochemical and genetic work. Some are edible, e.g. morels and truffles | Penicillium, yeast, Aspergillus, Claviceps and Neurospora |
| Basidiomycetes | Some are edible, e.g. mushrooms. Mushrooms are rich in protein | Agaricus (mushroom), Ustilago (smut) and Puccinia (rust fungus), Mushrooms, bracket fungi, puffballs |
| Deuteromycetes | They are known as ‘Imperfect Fungi’ because in this group, only asexual or vegetative phases are seen. Some fungi of this group are saprophytes or parasites while the majority are decomposers of litter, which aid in mineral cycling | Alternaria, Colletotrichum and Trichoderma |
All eukaryotic organisms that contain chlorophyll, usually known as plants, are classified as Plantae. A few species, like parasites and plants that feed on insects, are partially heterotrophic. Insectivorous plants include bladderwort and Venus fly traps, and parasites like Cuscuta feed on them. The eukaryotic structure of plant cells has large chloroplasts and a cell wall comprised primarily of cellulose. Algae, bryophytes, pteridophytes, gymnosperms, and angiosperms are all part of the plant kingdom.
The haploid gametophytic and the diploid sporophytic phases of a plant’s life cycle alternate with one another. Various plant families have different haploid and diploid phase lengths and whether they are independent or reliant on others.
They are multicellular and heterotrophic (show the holozoic mode of nutrition) eukaryotes. They lack cell walls. Almost, all the animals show locomotion. Sexual reproduction occurs by the fusion of male and female gametes which give rise to an embryo followed by repeated cell divisions.
The differences between viruses, viroids and prions are given below:
| Viruses | Viroids | Prions |
| They are oblique intracellular agents | They are oblique intracellular agents | They are the abnormal form of a cellular protein |
| They have either DNA or RNA which is surrounded by a protein coat | They consist of only RNA. The protein coat is absent | They don’t possess DNA or RNA. Only protein coat is present |
Bacteriophages are also known as phages. These are the viruses which infect and replicate in the bacterial cells.
The tobacco mosaic virus (TMV) consists of single-stranded RNA. It infects tobacco plants and members of the family Solanaceae. The infection can cause some patterns like a mosaic, which shows mottling and discolouration on the surface of the leaves.
The close association of fungus and algae form lichens. They are found in a pollution-free environment. Lichens are used in deodorant, pH papers, insense-sticks, toothpaste and perfumes. The fungal component is known as mycobiont and the algal component is known as phycobiont.
Answer:
Heterotrophic Bacteria: They help with nitrogen fixation, ammonification and nitrification. In addition, Rhizobium bacteria, they maintain soil fertility. Other members produce dairy products such as cheese and cottage cheese. Archaebacteria: Methanogens in animal feces produce biogas.
Answer:
Plant-like features are:
- Euglena has plastids which help in photosynthesis
- Some of the species of euglena have carotenoid pigments, which give it red colour
Animal-like features are:
- Euglena doesn’t have a cell wall
- Flagella are present for locomotion
Answer:
See lessMushroom and yeast are the most useful fungi. Mushrooms are edible and are a good source of proteins. Yeast is used to make bread and cheese. Penicillium fungi is used to produce antibiotics.
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 :
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 :
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 :
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:
Some Branch of Physics
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.
The other sciences, like geology, oceanology, seismology, etc, also use some laws of physics.
Sample Problems
Problem 1: What is “high-energy” physics?
Solution:
Problem 2: Explain the relation of physics to seismology.
Solution:
Problem 3: Differentiate between weak and strong nuclear forces.
Solution:
Problem 4: What is the difference between classical and modern physics?
Solution:
Problem 5: Define astrophysics.
Solution:
Problem 6: Explain the reasons behind the durability of scientific knowledge.
Solution:
Problem 7: Is it possible to modify a scientific theory?
Solution:
See less