If A = {1,2,3,4}, how many subsets in P(A) are equal to their own complement with respect to A?
Answer and explanation
Correct answer: 0
For any subset S of A, its complement A \ S contains exactly the elements of A that are not in S. If S were equal to its complement, each element would have to be both in S and not in S, which is impossible. Equivalently, S and its complement are disjoint, so they cannot be equal when A is non-empty. Thus the count is 0, option A.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
For any subset S of A, its complement A \ S contains exactly the elements of A that are not in S. If S were equal to its complement, each element would have to be both in S and not in S, which is impossible. Equivalently, S and its complement are disjoint, so they cannot be equal when A is non-empty. Thus the count is 0, option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
