If A ⊆ U, n(U) = 7, and n(P(A)) = 16, what is n(P(A′))?
Answer and explanation
Correct answer: 8
For a finite set X, the number of elements in its power set is n(P(X)) = 2ⁿ⁽ˣ⁾. Since n(P(A)) = 16 = 2⁴, we get n(A) = 4. The complement therefore has n(A′) = n(U) − n(A) = 7 − 4 = 3 elements. Hence n(P(A′)) = 2³ = 8. Option B is correct. The value 16 belongs to P(A), while 4 is n(A), not the requested power-set cardinality.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
For a finite set X, the number of elements in its power set is n(P(X)) = 2ⁿ⁽ˣ⁾. Since n(P(A)) = 16 = 2⁴, we get n(A) = 4. The complement therefore has n(A′) = n(U) − n(A) = 7 − 4 = 3 elements. Hence n(P(A′)) = 2³ = 8. Option B is correct. The value 16 belongs to P(A), while 4 is n(A), not the requested power-set cardinality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
