Let U = {1, 2, ..., 12}, A = {2, 4, 6, 8, 10, 12}, and B = {3, 6, 9, 12}. What is (A ∪ B)′?
Answer and explanation
Correct answer: {1, 5, 7, 11}
First form the union: A ∪ B = {2, 3, 4, 6, 8, 9, 10, 12}. The complement is taken relative to U, so it contains exactly those elements of U that are absent from the union. From {1, 2, ..., 12}, the elements not listed in A ∪ B are 1, 5, 7, and 11. Thus (A ∪ B)′ = {1, 5, 7, 11}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
{1, 5, 7, 11}
Why is this the correct answer?
First form the union: A ∪ B = {2, 3, 4, 6, 8, 9, 10, 12}. The complement is taken relative to U, so it contains exactly those elements of U that are absent from the union. From {1, 2, ..., 12}, the elements not listed in A ∪ B are 1, 5, 7, and 11. Thus (A ∪ B)′ = {1, 5, 7, 11}, making option A correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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