Let U = {1, 2, 3, ..., 16} and A = {x in U : x is divisible by 4}. What is the complement A' with respect to U?
Answer and explanation
Correct answer: {1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}
The elements of U divisible by 4 are 4, 8, 12, and 16, so A = {4, 8, 12, 16}. The complement A' consists of every element of U that is not in A. Removing those four multiples of 4 from U leaves {1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}. Thus option A is correct; option B is A itself.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}
Why is this the correct answer?
The elements of U divisible by 4 are 4, 8, 12, and 16, so A = {4, 8, 12, 16}. The complement A' consists of every element of U that is not in A. Removing those four multiples of 4 from U leaves {1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}. Thus option A is correct; option B is A itself.
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.
