If A = {p, q, r}, how many subsets of A must contain p?
Answer and explanation
Correct answer: 4
Since p must be present, it is fixed in every counted subset. The remaining elements q and r are optional, and each can independently be included or excluded. Therefore there are 2 choices for q and 2 choices for r, giving 2 × 2 = 4 subsets. They are {p}, {p, q}, {p, r}, and {p, q, r}. Equivalently, a three-element set has 2^3 subsets, and fixing p reduces the free choices to two elements, giving 2^2 = 4.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Since p must be present, it is fixed in every counted subset. The remaining elements q and r are optional, and each can independently be included or excluded. Therefore there are 2 choices for q and 2 choices for r, giving 2 × 2 = 4 subsets. They are {p}, {p, q}, {p, r}, and {p, q, r}. Equivalently, a three-element set has 2^3 subsets, and fixing p reduces the free choices to two elements, giving 2^2 = 4.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
