If A = {a,b,c,d,e}, how many elements of P(A) contain both a and b?
Answer and explanation
Correct answer: 8
The elements a and b must be included in every desired subset, so they are fixed choices. The remaining three elements c, d, and e may each either be included or omitted independently. Hence there are 2³ = 8 possible choices for the remaining elements. Every such choice produces one subset containing both a and b, so the required number of elements of P(A) is 8. Option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The elements a and b must be included in every desired subset, so they are fixed choices. The remaining three elements c, d, and e may each either be included or omitted independently. Hence there are 2³ = 8 possible choices for the remaining elements. Every such choice produces one subset containing both a and b, so the required number of elements of P(A) is 8. 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.
