If A = {1, 2, 3, 4, 5}, how many subsets of A contain 1 but do not contain 2?
Answer and explanation
Correct answer: 8
The element 1 is compulsory, so there is no choice about including it. The element 2 is forbidden, so it also gives no choice and must be left out. The remaining elements are 3, 4, and 5, and each of these may either be included or excluded independently. Thus the number of valid subsets is 2³ = 8. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The element 1 is compulsory, so there is no choice about including it. The element 2 is forbidden, so it also gives no choice and must be left out. The remaining elements are 3, 4, and 5, and each of these may either be included or excluded independently. Thus the number of valid subsets is 2³ = 8. Therefore, 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.
