If A={1,2} and B={2,3}, how many proper subsets are in P(A∪B)?
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Answer and explanation
Correct answer: 7
First find the union: A∪B={1,2,3}, which has three elements. Therefore its power set contains 2^3=8 subsets. A proper subset of a set is any subset other than the set itself, so exactly one subset, {1,2,3}, must be excluded. The number of proper subsets is 8−1=7; hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
First find the union: A∪B={1,2,3}, which has three elements. Therefore its power set contains 2^3=8 subsets. A proper subset of a set is any subset other than the set itself, so exactly one subset, {1,2,3}, must be excluded. The number of proper subsets is 8−1=7; 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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