If A = {1, 2, {3, 4}}, which of the following must be an element of P(A)?
Answer and explanation
Correct answer: {{3, 4}}
The elements of A are 1, 2, and the single object {3,4}. The power set P(A) contains exactly the subsets of A. Since {3,4} is one element of A, the set containing that element alone, namely {{3,4}}, is a subset of A and therefore belongs to P(A). In contrast, 3 and 4 are not separate elements of A, so the other listed sets are not necessarily subsets. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
{{3, 4}}
Why is this the correct answer?
The elements of A are 1, 2, and the single object {3,4}. The power set P(A) contains exactly the subsets of A. Since {3,4} is one element of A, the set containing that element alone, namely {{3,4}}, is a subset of A and therefore belongs to P(A). In contrast, 3 and 4 are not separate elements of A, so the other listed sets are not necessarily subsets. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
