If n(P(A′)) = 64 and the universal set U has n(U) = 10, what is n(A)?
Answer and explanation
Correct answer: 4
For every finite set X, n(P(X)) = 2ⁿ⁽ˣ⁾. Thus 64 = 2⁶ gives n(A′) = 6. Because A′ is the complement of A within U, A and A′ partition U, so n(A) + n(A′) = n(U). Therefore n(A) = 10 − 6 = 4. Option A is correct. The value 6 is the cardinality of the complement, not of A; the other values do not satisfy the power-set relation.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For every finite set X, n(P(X)) = 2ⁿ⁽ˣ⁾. Thus 64 = 2⁶ gives n(A′) = 6. Because A′ is the complement of A within U, A and A′ partition U, so n(A) + n(A′) = n(U). Therefore n(A) = 10 − 6 = 4. Option A is correct. The value 6 is the cardinality of the complement, not of A; the other values do not satisfy the power-set relation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
