If A = {x ∈ ℤ : 2x + 1 is even}, what is A?
Answer and explanation
Correct answer: A = ∅
For every integer x, the product 2x is even. Adding 1 to an even integer always produces an odd integer, so 2x + 1 can never be even. Consequently, there is no integer satisfying the defining condition of A. A set with no elements is called the empty set and is denoted by ∅. Therefore A = ∅, making option A the only correct answer.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
For every integer x, the product 2x is even. Adding 1 to an even integer always produces an odd integer, so 2x + 1 can never be even. Consequently, there is no integer satisfying the defining condition of A. A set with no elements is called the empty set and is denoted by ∅. Therefore A = ∅, making option A the only correct answer.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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