If A = {x : x ∈ Z and |x| ≤ 2} and B = {-2, -1, 0, 1, 2}, which conclusion is correct?
Answer and explanation
Correct answer: A = B
For an integer x, the inequality |x| ≤ 2 means that x lies between -2 and 2 inclusive. The integers satisfying this condition are -2, -1, 0, 1, and 2. Hence A = {-2, -1, 0, 1, 2}, which is exactly the given set B. Therefore A = B. Option B omits the negative integers, option D omits the values between the endpoints, and option C is false because the two sets are equal rather than properly contained.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
For an integer x, the inequality |x| ≤ 2 means that x lies between -2 and 2 inclusive. The integers satisfying this condition are -2, -1, 0, 1, and 2. Hence A = {-2, -1, 0, 1, 2}, which is exactly the given set B. Therefore A = B. Option B omits the negative integers, option D omits the values between the endpoints, and option C is false because the two sets are equal rather than properly contained.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
