For A = {x ∈ Z : (x − 2)(x + 3) = 0} and B = {-3, 2}, which conclusion is correct?
Answer and explanation
Correct answer: A = B
A product is zero when at least one factor is zero. Thus (x − 2)(x + 3) = 0 gives x − 2 = 0 or x + 3 = 0, so x = 2 or x = -3. Both values belong to the integers, and hence A = {2, -3}. Since the order of elements does not affect a set, {2, -3} = {-3, 2} = B. Therefore, A = B. The set has only two elements, so it is finite, not infinite.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
A product is zero when at least one factor is zero. Thus (x − 2)(x + 3) = 0 gives x − 2 = 0 or x + 3 = 0, so x = 2 or x = -3. Both values belong to the integers, and hence A = {2, -3}. Since the order of elements does not affect a set, {2, -3} = {-3, 2} = B. Therefore, A = B. The set has only two elements, so it is finite, not infinite.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
