If I₁ = {x : x ∈ ℤ, x/2 ∈ ℤ, −5 < x < 5}, what is I₁?
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Answer and explanation
Correct answer: I₁ = {−4, −2, 0, 2, 4}
Since x/2 is an integer, x must be divisible by 2; therefore x must be an even integer. The strict inequality −5 < x < 5 allows the integers −4 through 4, but among them the even integers are −4, −2, 0, 2, and 4. Zero is included because 0/2 = 0, which is an integer. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
I₁ = {−4, −2, 0, 2, 4}
Why is this the correct answer?
Since x/2 is an integer, x must be divisible by 2; therefore x must be an even integer. The strict inequality −5 < x < 5 allows the integers −4 through 4, but among them the even integers are −4, −2, 0, 2, and 4. Zero is included because 0/2 = 0, which is an integer. Thus 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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