If A = {1,2,3,4,5}, how many subsets in P(A) either contain both 2 and 3 or contain neither of them?
Answer and explanation
Correct answer: 16
For the two elements 2 and 3, the condition allows exactly two possibilities: both are selected, or neither is selected. The other three elements, 1, 4, and 5, can each be selected or omitted independently, giving 2³ = 8 choices. Multiplying by the 2 allowed cases for the pair gives 2 × 8 = 16 subsets. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
For the two elements 2 and 3, the condition allows exactly two possibilities: both are selected, or neither is selected. The other three elements, 1, 4, and 5, can each be selected or omitted independently, giving 2³ = 8 choices. Multiplying by the 2 allowed cases for the pair gives 2 × 8 = 16 subsets. Hence, 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.
