If U = {1, 2, ..., 30}, A = {x : x is even}, and B = {x : x is prime}, what is |A' ∩ B'|?
Answer and explanation
Correct answer: 6
A' contains the odd numbers, while B' contains the non-prime numbers. Therefore, A' ∩ B' consists of odd composite numbers and 1, because 1 is not prime. From 1 to 30, these elements are {1, 9, 15, 21, 25, 27}. The number 1 must not be excluded merely because it is neither prime nor composite; it is non-prime. Hence the cardinality is 6, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A' contains the odd numbers, while B' contains the non-prime numbers. Therefore, A' ∩ B' consists of odd composite numbers and 1, because 1 is not prime. From 1 to 30, these elements are {1, 9, 15, 21, 25, 27}. The number 1 must not be excluded merely because it is neither prime nor composite; it is non-prime. Hence the cardinality is 6, so 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.
