If A = {1, 2, 3, 4, 5}, how many subsets of A contain both 2 and 5?
Answer and explanation
Correct answer: 8
The elements 2 and 5 must be included in every required subset, so their choices are fixed. The remaining elements 1, 3, and 4 are unrestricted; each can either be included or excluded independently. Therefore, the number of subsets is 2 × 2 × 2 = 2³ = 8. This is a standard subset-counting rule: if k elements are free, there are 2ᵏ possible choices.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The elements 2 and 5 must be included in every required subset, so their choices are fixed. The remaining elements 1, 3, and 4 are unrestricted; each can either be included or excluded independently. Therefore, the number of subsets is 2 × 2 × 2 = 2³ = 8. This is a standard subset-counting rule: if k elements are free, there are 2ᵏ possible choices.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
