If A = {x ∈ Z : |x| ≤ 4} and B = {x ∈ Z : x² − 2x − 3 = 0}, how many elements does A \ B contain?
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Answer and explanation
Correct answer: 7
The condition |x| ≤ 4 gives A = {−4, −3, −2, −1, 0, 1, 2, 3, 4}, which has 9 elements. Factor the equation for B: x² − 2x − 3 = (x − 3)(x + 1) = 0, so B = {3, −1}. Both elements of B belong to A, and removing them leaves 9 − 2 = 7 elements. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The condition |x| ≤ 4 gives A = {−4, −3, −2, −1, 0, 1, 2, 3, 4}, which has 9 elements. Factor the equation for B: x² − 2x − 3 = (x − 3)(x + 1) = 0, so B = {3, −1}. Both elements of B belong to A, and removing them leaves 9 − 2 = 7 elements. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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