If A = {2,4,6,8,10}, how many elements of P(A) contain only even numbers?
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Answer and explanation
Correct answer: 32
Every element of A is even. Every member of P(A) is a subset of A, so it can contain no numbers other than these even elements. Since A has five elements, the number of its subsets is 2⁵ = 32, including the empty set and A itself. Therefore, 32 members of P(A) contain only even numbers.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
Every element of A is even. Every member of P(A) is a subset of A, so it can contain no numbers other than these even elements. Since A has five elements, the number of its subsets is 2⁵ = 32, including the empty set and A itself. Therefore, 32 members of P(A) contain only even numbers.
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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