If A = {a, b, c, d, e}, how many elements of P(A) contain exactly one of a and b and also contain e?
Answer and explanation
Correct answer: 8
A subset must contain exactly one of a and b, so there are 2 choices: select a but not b, or select b but not a. The element e is required, so it has only one choice and must be included. The elements c and d are unrestricted; each may be included or excluded independently, giving 2^2 = 4 choices. Therefore the total is 2 × 4 = 8, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A subset must contain exactly one of a and b, so there are 2 choices: select a but not b, or select b but not a. The element e is required, so it has only one choice and must be included. The elements c and d are unrestricted; each may be included or excluded independently, giving 2^2 = 4 choices. Therefore the total is 2 × 4 = 8, 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.
