If A = {1, 2, 3, 4}, how many members of the power set P(A) are disjoint from {1, 2}?
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Answer and explanation
Correct answer: 4
A subset of A is disjoint from {1, 2} only when it contains neither 1 nor 2. Therefore, every such subset must be formed from the remaining elements {3, 4}. Each of these two elements may either be selected or not selected, giving 2^2 = 4 possible subsets: empty set, {3}, {4}, and {3, 4}. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A subset of A is disjoint from {1, 2} only when it contains neither 1 nor 2. Therefore, every such subset must be formed from the remaining elements {3, 4}. Each of these two elements may either be selected or not selected, giving 2^2 = 4 possible subsets: empty set, {3}, {4}, and {3, 4}. 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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