If A = {1, 2, 3, 4}, how many subsets of A contain the element 2?
Answer and explanation
Correct answer: 8
The element 2 must be included in every required subset, so it is not a choice. The remaining elements 1, 3, and 4 can each independently be included or excluded. Thus there are 2 choices for each of three elements, giving 2³ = 8 subsets. Equivalently, a four-element set has 2⁴ = 16 total subsets, and exactly half contain any fixed element, so 16 ÷ 2 = 8.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The element 2 must be included in every required subset, so it is not a choice. The remaining elements 1, 3, and 4 can each independently be included or excluded. Thus there are 2 choices for each of three elements, giving 2³ = 8 subsets. Equivalently, a four-element set has 2⁴ = 16 total subsets, and exactly half contain any fixed element, so 16 ÷ 2 = 8.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
