If A = {p, q, r}, how many elements of P(A) must contain p?
Answer and explanation
Correct answer: 4
Every subset counted must include p, so p is fixed and cannot be chosen independently. The remaining elements q and r can each either be included or excluded. Thus there are 2 choices for q and 2 choices for r, giving 2 × 2 = 2² = 4 subsets. They are {p}, {p, q}, {p, r}, and {p, q, r}. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Every subset counted must include p, so p is fixed and cannot be chosen independently. The remaining elements q and r can each either be included or excluded. Thus there are 2 choices for q and 2 choices for r, giving 2 × 2 = 2² = 4 subsets. They are {p}, {p, q}, {p, r}, and {p, q, r}. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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