If A = {x ∈ R : x ≠ 0} and B = {x ∈ R : x² > 0}, what is A △ B?
Answer and explanation
Correct answer: ∅
For a real number x, the inequality x² > 0 holds exactly when x is nonzero. If x = 0, then x² = 0, and if x ≠ 0, then x² is positive. Thus A and B describe exactly the same set, namely R − {0}. The symmetric difference contains elements belonging to exactly one set, so equal sets have symmetric difference ∅. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
For a real number x, the inequality x² > 0 holds exactly when x is nonzero. If x = 0, then x² = 0, and if x ≠ 0, then x² is positive. Thus A and B describe exactly the same set, namely R − {0}. The symmetric difference contains elements belonging to exactly one set, so equal sets have symmetric difference ∅. 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).
