If U = {a,b,c,d,e,f,g,h} and A = {a,b,c}, how many members of P(U) contain A as a subset?
Answer and explanation
Correct answer: 32
Every member of P(U) that contains A must include a, b, and c. The remaining elements d, e, f, g, and h are optional; each may be included or omitted independently. Thus the required subsets have the form A ∪ S, where S is any subset of U − A. Since U − A has 5 elements, the number of possibilities is 2⁵ = 32. Option C is correct.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
Every member of P(U) that contains A must include a, b, and c. The remaining elements d, e, f, g, and h are optional; each may be included or omitted independently. Thus the required subsets have the form A ∪ S, where S is any subset of U − A. Since U − A has 5 elements, the number of possibilities is 2⁵ = 32. Option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
