If A = {a, b, c, d}, how many elements of the power set P(A) are not disjoint from {a, d}?
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Answer and explanation
Correct answer: 12
The power set of A has 2^4 = 16 subsets in total. A subset is disjoint from {a, d} only when it contains neither a nor d; therefore, it can be formed using only b and c. There are 2^2 = 4 such disjoint subsets. The subsets that are not disjoint are the remaining 16 − 4 = 12 subsets. Thus, option C is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The power set of A has 2^4 = 16 subsets in total. A subset is disjoint from {a, d} only when it contains neither a nor d; therefore, it can be formed using only b and c. There are 2^2 = 4 such disjoint subsets. The subsets that are not disjoint are the remaining 16 − 4 = 12 subsets. Thus, option C 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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