If U = {a, b, c, d}, A = {a, b}, and B = {b, c}, what is (A ∩ B)'?
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Answer and explanation
Correct answer: {a, c, d}
First find the intersection of A and B. The only element common to A = {a,b} and B = {b,c} is b, so A ∩ B = {b}. The complement is taken relative to U = {a,b,c,d}; therefore, (A ∩ B)' consists of every element of U except b. Hence, (A ∩ B)' = {a,c,d}, which is option B.
Frequently asked questions
What is the correct answer to this question?
{a, c, d}
Why is this the correct answer?
First find the intersection of A and B. The only element common to A = {a,b} and B = {b,c} is b, so A ∩ B = {b}. The complement is taken relative to U = {a,b,c,d}; therefore, (A ∩ B)' consists of every element of U except b. Hence, (A ∩ B)' = {a,c,d}, which is option 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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