If A = {0, 1, 2, 3}, how many subsets of A must contain 0?
Answer and explanation
Correct answer: 8
The element 0 is required to be in every counted subset, so its inclusion is fixed and creates only one choice. The remaining three elements, 1, 2, and 3, may each either be included or excluded independently. Thus there are 2 choices for each of three elements, giving 2 × 2 × 2 = 2³ = 8 subsets. Equivalently, exactly half of the 2⁴ = 16 subsets of A contain any particular fixed element. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The element 0 is required to be in every counted subset, so its inclusion is fixed and creates only one choice. The remaining three elements, 1, 2, and 3, may each either be included or excluded independently. Thus there are 2 choices for each of three elements, giving 2 × 2 × 2 = 2³ = 8 subsets. Equivalently, exactly half of the 2⁴ = 16 subsets of A contain any particular fixed element. Therefore option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
