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Few More Examples of Sets Video Lecture | Sets and Functions - JEE

Q: 3. What is the cardinality of a set?

Ans. The cardinality of a set is the number of elements it contains. It is denoted by the symbol |A|, where A is the set. For example, if A = {1, 2, 3}, then |A| = 3. If a set has no elements, it is called an empty set or a null set, and its cardinality is 0.

Q: 4. What is the intersection of sets?

Ans. The intersection of two sets A and B is the set of elements that are common to both A and B. It is denoted by A ∩ B. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}. If the intersection of two sets is empty, it means they have no common elements.

Q: 5. What is the power set of a set?

Ans. The power set of a set A is the set of all possible subsets of A, including the empty set and the set itself. It is denoted by P(A). For example, if A = {1, 2}, then P(A) = {{}, {1}, {2}, {1, 2}}. The power set of a set with n elements has 2^n elements.

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FAQs on Few More Examples of Sets Video Lecture - Sets and Functions - JEE

1. What is a set in mathematics?

Ans. A set in mathematics is a collection of distinct objects, which can be numbers, letters, or any other entities. These objects are called elements or members of the set. For example, the set of all natural numbers {1, 2, 3, 4, ...} is a collection of distinct numbers.

2. How are sets represented?

Ans. Sets are usually represented by listing their elements within curly braces {}. For example, the set of all even numbers can be represented as {2, 4, 6, 8, ...}. Sets can also be represented using set-builder notation, where the elements are defined based on certain properties. For example, the set of all positive integers less than 10 can be represented as {x | x is a positive integer and x < 10}.

3. What is the cardinality of a set?

Ans. The cardinality of a set is the number of elements it contains. It is denoted by the symbol |A|, where A is the set. For example, if A = {1, 2, 3}, then |A| = 3. If a set has no elements, it is called an empty set or a null set, and its cardinality is 0.

4. What is the intersection of sets?

Ans. The intersection of two sets A and B is the set of elements that are common to both A and B. It is denoted by A ∩ B. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}. If the intersection of two sets is empty, it means they have no common elements.

5. What is the power set of a set?

Ans. The power set of a set A is the set of all possible subsets of A, including the empty set and the set itself. It is denoted by P(A). For example, if A = {1, 2}, then P(A) = {{}, {1}, {2}, {1, 2}}. The power set of a set with n elements has 2^n elements.

Text Transcript from Video

let's discuss a few more examples of
sets consider the collection of odd
natural numbers less than five clearly
this collection is well-defined and will
include numbers 1 & 3 the set of types
of fingers will include the names index
middle ring and pinkie
the set of prime factors of 15 will
include the numbers 3 & 5 the set of
letters forming the word fun includes
the letters and U and F the set of
months of a year beginning with the
letter M includes two elements March and
May

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