If V = {x : x ∈ ℤ, x/2 ∈ ℕ, −5 < x < 7}, then V is:
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Answer and explanation
Correct answer: V = {2, 4, 6}
Because x/2 must be a natural number, x must be twice a positive natural number; therefore x is a positive even integer. The interval −5 < x < 7 contains the even integers −4, −2, 0, 2, 4, and 6, but only 2, 4, and 6 produce positive natural quotients. Thus V = {2, 4, 6}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
V = {2, 4, 6}
Why is this the correct answer?
Because x/2 must be a natural number, x must be twice a positive natural number; therefore x is a positive even integer. The interval −5 < x < 7 contains the even integers −4, −2, 0, 2, 4, and 6, but only 2, 4, and 6 produce positive natural quotients. Thus V = {2, 4, 6}, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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