If U = {1,2,…,20}, A = {x : x is even}, and B = {x : x is prime}, how many elements are in A′ ∩ B′?
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Answer and explanation
Correct answer: 3
A′ contains the odd numbers, while B′ contains the non-prime numbers. We need numbers from 1 to 20 that are both odd and non-prime. They are 1, 9, and 15. Note that 1 is not prime, and 3, 5, 7, 11, 13, 17, and 19 are excluded because they are prime. Thus A′ ∩ B′ = {1,9,15}, whose cardinality is 3.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
A′ contains the odd numbers, while B′ contains the non-prime numbers. We need numbers from 1 to 20 that are both odd and non-prime. They are 1, 9, and 15. Note that 1 is not prime, and 3, 5, 7, 11, 13, 17, and 19 are excluded because they are prime. Thus A′ ∩ B′ = {1,9,15}, whose cardinality is 3.
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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