If U = {a, b, c, d, e, f, g, i, j, k}, A' = {b, e, i}, and B' = {a, d, j}, what is (A ∪ B)'?
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Answer and explanation
Correct answer: ∅
By De Morgan’s law, (A ∪ B)' = A' ∩ B'. The given sets A' = {b, e, i} and B' = {a, d, j} have no common element. Their intersection is therefore empty: A' ∩ B' = ∅. Hence (A ∪ B)' = ∅, so option A is correct. The other listed sets either combine elements or select only one complement.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
By De Morgan’s law, (A ∪ B)' = A' ∩ B'. The given sets A' = {b, e, i} and B' = {a, d, j} have no common element. Their intersection is therefore empty: A' ∩ B' = ∅. Hence (A ∪ B)' = ∅, so option A is correct. The other listed sets either combine elements or select only one complement.
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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