If U = {1,2,3,4,5,6,7,8,9,10} and A = {x : x ∈ U, x is even}, how many non-empty members are in P(A′)?
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Answer and explanation
Correct answer: 31
The set A contains the even numbers {2,4,6,8,10}. Therefore, its complement in U is A′ = {1,3,5,7,9}, which has 5 elements. A set with 5 elements has 2⁵ = 32 subsets in its power set. One of these subsets is the empty set, so the number of non-empty members is 32 − 1 = 31. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
31
Why is this the correct answer?
The set A contains the even numbers {2,4,6,8,10}. Therefore, its complement in U is A′ = {1,3,5,7,9}, which has 5 elements. A set with 5 elements has 2⁵ = 32 subsets in its power set. One of these subsets is the empty set, so the number of non-empty members is 32 − 1 = 31. 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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