If the universal set U = {1, 2, 3, 4, 5, 6} and A = {1, 5, 6}, what is A − A′?
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Answer and explanation
Correct answer: {1, 5, 6}
Relative to U, the complement of A is A′ = {2, 3, 4}. Since A and A′ are disjoint, none of the elements removed from A belongs to A′. Therefore, A − A′ leaves A unchanged, so A − A′ = A = {1, 5, 6}. Do not confuse this difference with A ∩ A′, which would be empty.
Frequently asked questions
What is the correct answer to this question?
{1, 5, 6}
Why is this the correct answer?
Relative to U, the complement of A is A′ = {2, 3, 4}. Since A and A′ are disjoint, none of the elements removed from A belongs to A′. Therefore, A − A′ leaves A unchanged, so A − A′ = A = {1, 5, 6}. Do not confuse this difference with A ∩ A′, which would be empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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