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If A = {1, 3, 5} then find the cardinality of the power set of A ?
- a)2
- b)8
- c)9
- d)6
- e)Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If A = {1, 3, 5} then find the cardinality of the power set of A ?a)2b...
CALCULATION:
Given: A = {1, 3, 5}
Here, we have to find the cardinality of the power set of A i.e n (P(A))
As we know that if A is a finite set with m elements. Then the number of elements (cardinality) of the power set of A is given by: n (P(A)) = 2m.
Here, we can see that, the given A has 3 elements i.e n(A) = 3
So, the cardinality of the given set is n(P(A)) = 23 = 8
Hence, the correct option is 4.
Most Upvoted Answer
If A = {1, 3, 5} then find the cardinality of the power set of A ?a)2b...
Explanation:
To find the cardinality of the power set of a set A, we need to find the number of all possible subsets of A.
The set A = {1, 3, 5} has 3 elements.
The power set of A will contain all possible subsets of A, including the empty set and the set A itself.
Empty set:
The empty set is a subset of every set, including A. Therefore, it will be included in the power set.
Single-element subsets:
For each element in A, we can have a subset containing only that element. In this case, we have 3 elements in A, so we will have 3 single-element subsets.
Two-element subsets:
For each pair of elements in A, we can have a subset containing those two elements. In this case, we have 3 elements in A, so we can choose 2 elements in C(3,2) = 3 ways. Therefore, we will have 3 two-element subsets.
Three-element subset:
The set A itself is a three-element subset.
Therefore, the power set of A will contain:
- 1 empty set
- 3 single-element subsets
- 3 two-element subsets
- 1 three-element subset
The total number of subsets in the power set is 1 + 3 + 3 + 1 = 8.
Hence, the cardinality of the power set of A is 8.
Answer:
The correct answer is option B) 8.
To find the cardinality of the power set of a set A, we need to find the number of all possible subsets of A.
The set A = {1, 3, 5} has 3 elements.
The power set of A will contain all possible subsets of A, including the empty set and the set A itself.
Empty set:
The empty set is a subset of every set, including A. Therefore, it will be included in the power set.
Single-element subsets:
For each element in A, we can have a subset containing only that element. In this case, we have 3 elements in A, so we will have 3 single-element subsets.
Two-element subsets:
For each pair of elements in A, we can have a subset containing those two elements. In this case, we have 3 elements in A, so we can choose 2 elements in C(3,2) = 3 ways. Therefore, we will have 3 two-element subsets.
Three-element subset:
The set A itself is a three-element subset.
Therefore, the power set of A will contain:
- 1 empty set
- 3 single-element subsets
- 3 two-element subsets
- 1 three-element subset
The total number of subsets in the power set is 1 + 3 + 3 + 1 = 8.
Hence, the cardinality of the power set of A is 8.
Answer:
The correct answer is option B) 8.
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If A = {1, 3, 5} then find the cardinality of the power set of A ?a)2b)8c)9d)6e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A = {1, 3, 5} then find the cardinality of the power set of A ?a)2b)8c)9d)6e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A = {1, 3, 5} then find the cardinality of the power set of A ?a)2b)8c)9d)6e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
If A = {1, 3, 5} then find the cardinality of the power set of A ?a)2b)8c)9d)6e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A = {1, 3, 5} then find the cardinality of the power set of A ?a)2b)8c)9d)6e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A = {1, 3, 5} then find the cardinality of the power set of A ?a)2b)8c)9d)6e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
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