If A = {a, b, c, d} and B = {c, d, e, f}, what is (A ∪ B) \ (A ∩ B)?
Answer and explanation
Correct answer: {a, b, e, f}
The union A ∪ B contains every distinct element from both sets, so A ∪ B = {a, b, c, d, e, f}. The intersection A ∩ B contains only the common elements, giving {c, d}. Set difference removes the elements of the second set from the first; therefore removing c and d from the union leaves {a, b, e, f}. Thus option A is correct. The other choices represent the intersection, the full union, or an empty result.
Frequently asked questions
What is the correct answer to this question?
{a, b, e, f}
Why is this the correct answer?
The union A ∪ B contains every distinct element from both sets, so A ∪ B = {a, b, c, d, e, f}. The intersection A ∩ B contains only the common elements, giving {c, d}. Set difference removes the elements of the second set from the first; therefore removing c and d from the union leaves {a, b, e, f}. Thus option A is correct. The other choices represent the intersection, the full union, or an empty result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
