If A={p,q,r,s}, how many elements of P(A) do not contain p?
Answer and explanation
Correct answer: 8
A subset that does not contain p can be formed only from the other three elements q, r, and s. Each of these three elements has two independent possibilities: it may be included or excluded. Therefore the number of permissible subsets is 2^3=8. These include the empty set, all single-element choices, all two-element choices, and the set {q,r,s}. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A subset that does not contain p can be formed only from the other three elements q, r, and s. Each of these three elements has two independent possibilities: it may be included or excluded. Therefore the number of permissible subsets is 2^3=8. These include the empty set, all single-element choices, all two-element choices, and the set {q,r,s}. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
