If W = {x ∈ Z : −3 ≤ x ≤ 3 and x² is even}, what is W?
Answer and explanation
Correct answer: English: W = {-2, 0, 2} | हिन्दी: W = {-2, 0, 2}
The integers satisfying −3 ≤ x ≤ 3 are −3, −2, −1, 0, 1, 2, and 3. The square of an integer is even exactly when the integer itself is even, because an even number has an even factor and an odd number has an odd square. Among the listed integers, the even values are −2, 0, and 2. Therefore W = {-2, 0, 2}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
English: W = {-2, 0, 2} | हिन्दी: W = {-2, 0, 2}
Why is this the correct answer?
The integers satisfying −3 ≤ x ≤ 3 are −3, −2, −1, 0, 1, 2, and 3. The square of an integer is even exactly when the integer itself is even, because an even number has an even factor and an odd number has an odd square. Among the listed integers, the even values are −2, 0, and 2. Therefore W = {-2, 0, 2}, 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.
