If U = {1, 2, ..., 18}, A = {2, 4, 6, 8, 10, 12, 14, 16, 18}, and B = {3, 6, 9, 12, 15, 18}, what is A′ ∪ B′?
Answer and explanation
Correct answer: {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17}
Apply De Morgan’s law: A′ ∪ B′ = (A ∩ B)′. The elements common to A and B are 6, 12, and 18, so A ∩ B = {6, 12, 18}. Taking the complement relative to U means removing these three elements from {1, ..., 18}. The remaining elements are {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17}. Hence option A is correct; option C would represent A′ ∩ B′ instead.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17}
Why is this the correct answer?
Apply De Morgan’s law: A′ ∪ B′ = (A ∩ B)′. The elements common to A and B are 6, 12, and 18, so A ∩ B = {6, 12, 18}. Taking the complement relative to U means removing these three elements from {1, ..., 18}. The remaining elements are {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17}. Hence option A is correct; option C would represent A′ ∩ B′ instead.
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.
