Let U = {1, 2, 3, ..., 20} and A = {x ∈ U : x is divisible by 4}. What is Aᶜ ∩ {x ∈ U : x is even}?
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Answer and explanation
Correct answer: {2, 6, 10, 14, 18}
Within U, the multiples of 4 are A = {4, 8, 12, 16, 20}. Its complement contains the numbers from 1 to 20 that are not divisible by 4. Intersecting this complement with the even numbers keeps only even numbers that are not multiples of 4: 2, 6, 10, 14, and 18. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
{2, 6, 10, 14, 18}
Why is this the correct answer?
Within U, the multiples of 4 are A = {4, 8, 12, 16, 20}. Its complement contains the numbers from 1 to 20 that are not divisible by 4. Intersecting this complement with the even numbers keeps only even numbers that are not multiples of 4: 2, 6, 10, 14, and 18. Therefore, option A is correct.
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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