If A = {a,b,c,d,e}, how many elements of P(A) contain at least one of a or b?
Answer and explanation
Correct answer: 24
There are 2⁵ = 32 total subsets of A. It is easier to count the complement: subsets containing neither a nor b. Such subsets can use only c, d, and e, and each of these three elements may be chosen or omitted, giving 2³ = 8 subsets. Therefore the number containing at least one of a or b is 32 − 8 = 24. This includes subsets containing a only, b only, or both, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
There are 2⁵ = 32 total subsets of A. It is easier to count the complement: subsets containing neither a nor b. Such subsets can use only c, d, and e, and each of these three elements may be chosen or omitted, giving 2³ = 8 subsets. Therefore the number containing at least one of a or b is 32 − 8 = 24. This includes subsets containing a only, b only, or both, 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.
