If A = {1, 2, 3, 4, 5, 6}, how many elements of the power set P(A) contain 1 and do not contain 6?
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Answer and explanation
Correct answer: 16
A subset of A must include 1, so that choice is fixed. It must exclude 6, so that choice is also fixed. The remaining four elements, namely 2, 3, 4, and 5, may each be either included or excluded independently. Therefore, the number of valid subsets is 2^4 = 16. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
A subset of A must include 1, so that choice is fixed. It must exclude 6, so that choice is also fixed. The remaining four elements, namely 2, 3, 4, and 5, may each be either included or excluded independently. Therefore, the number of valid subsets is 2^4 = 16. 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.
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