Let U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, and B = {3, 4, 5}. What is A' ∩ B'?
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Answer and explanation
Correct answer: {6}
Complements must be taken relative to the universal set U. Thus A' = U − A = {4,5,6}, while B' = U − B = {1,2,6}. The elements common to both complements are found by intersection: {4,5,6} ∩ {1,2,6} = {6}. Therefore, A' ∩ B' = {6}. This also agrees with De Morgan's law: A' ∩ B' = (A ∪ B)'.
Frequently asked questions
What is the correct answer to this question?
{6}
Why is this the correct answer?
Complements must be taken relative to the universal set U. Thus A' = U − A = {4,5,6}, while B' = U − B = {1,2,6}. The elements common to both complements are found by intersection: {4,5,6} ∩ {1,2,6} = {6}. Therefore, A' ∩ B' = {6}. This also agrees with De Morgan's law: A' ∩ B' = (A ∪ B)'.
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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