If A = {p, q, r, s, t, u}, how many subsets of A contain neither p nor q?
Answer and explanation
Correct answer: 16
The condition ‘neither p nor q’ means that both p and q must be excluded from every valid subset. The only elements available for selection are r, s, t, and u, giving four independently optional elements. Each can be either selected or not selected, so the number of subsets is 2⁴ = 16. This includes the empty subset. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The condition ‘neither p nor q’ means that both p and q must be excluded from every valid subset. The only elements available for selection are r, s, t, and u, giving four independently optional elements. Each can be either selected or not selected, so the number of subsets is 2⁴ = 16. This includes the empty subset. Hence, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
