If A has 5 elements, how many subsets of A do not contain two specified elements?
Answer and explanation
Correct answer: 8
The two specified elements are forbidden, so they cannot be selected in any valid subset. The remaining 5 − 2 = 3 elements are unrestricted; each may independently be included or excluded. Therefore the number of valid subsets is 2^3 = 8. This includes the empty subset and all allowed combinations of the remaining three elements, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The two specified elements are forbidden, so they cannot be selected in any valid subset. The remaining 5 − 2 = 3 elements are unrestricted; each may independently be included or excluded. Therefore the number of valid subsets is 2^3 = 8. This includes the empty subset and all allowed combinations of the remaining three elements, so 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.
