If U = {a, b, c, d, e, f, g} and A = {a, c, e}, how many members of P(U) contain A as a subset?
Answer and explanation
Correct answer: 16
A member S of P(U) contains A as a subset when every element of A, namely a, c, and e, is already included in S. The remaining elements b, d, f, and g are optional; each may be included or excluded independently. Thus there are 2^4 = 16 possible choices for the optional elements. Hence 16 members of P(U) contain A, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
A member S of P(U) contains A as a subset when every element of A, namely a, c, and e, is already included in S. The remaining elements b, d, f, and g are optional; each may be included or excluded independently. Thus there are 2^4 = 16 possible choices for the optional elements. Hence 16 members of P(U) contain A, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
