If U = {1, 2, ..., 12} and A = {x : x is a divisor of 12}, what is A'?
Answer and explanation
Correct answer: {5, 7, 8, 9, 10, 11}
The positive divisors of 12 that lie in U are A = {1, 2, 3, 4, 6, 12}. The complement A' contains every element of U that is not in A. Removing these divisors from {1, 2, ..., 12} leaves {5, 7, 8, 9, 10, 11}. Therefore option A is correct. The universal set is essential when finding a complement.
Frequently asked questions
What is the correct answer to this question?
{5, 7, 8, 9, 10, 11}
Why is this the correct answer?
The positive divisors of 12 that lie in U are A = {1, 2, 3, 4, 6, 12}. The complement A' contains every element of U that is not in A. Removing these divisors from {1, 2, ..., 12} leaves {5, 7, 8, 9, 10, 11}. Therefore option A is correct. The universal set is essential when finding a complement.
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.
