If A = {2, 4, 6} and B = {6, 8, 10}, how many elements does the power set P(A ∪ B) have?
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Answer and explanation
Correct answer: 32
The common element 6 must be counted only once in the union. Therefore, A ∪ B = {2, 4, 6, 8, 10}, which has 5 elements. A set with n elements has 2^n subsets in its power set, including the empty set and the set itself. Hence |P(A ∪ B)| = 2^5 = 32. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The common element 6 must be counted only once in the union. Therefore, A ∪ B = {2, 4, 6, 8, 10}, which has 5 elements. A set with n elements has 2^n subsets in its power set, including the empty set and the set itself. Hence |P(A ∪ B)| = 2^5 = 32. Therefore, 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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