If A = {1, 2, 3, 4, 5}, how many subsets of A contain neither 1 nor 2?
Answer and explanation
Correct answer: 8
A subset that contains neither 1 nor 2 can use only the remaining elements 3, 4, and 5. Each of these three elements may independently be selected or not selected. Therefore the number of such subsets is 2³ = 8. This includes the empty set, single-element subsets, larger permitted subsets, and {3,4,5}; hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A subset that contains neither 1 nor 2 can use only the remaining elements 3, 4, and 5. Each of these three elements may independently be selected or not selected. Therefore the number of such subsets is 2³ = 8. This includes the empty set, single-element subsets, larger permitted subsets, and {3,4,5}; 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.
