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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 20

If \(U=\{1,2,3,\ldots,20\}\), \(A=\{x:x\text{ is prime}\}\), and \(B=\{x:x\text{ is odd}\}\), what is \(A^c\cap B\)?

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Answer and explanation

Correct answer: \(\{1,9,15\}\)

The set \(B\) consists of all odd numbers from 1 to 20. The odd prime numbers in this range are 3, 5, 7, 11, 13, 17, and 19. Removing these from B leaves the odd, non-prime numbers \(\{1,9,15\}\). Note that 1 is not prime, because a prime number must have exactly two distinct positive divisors.

Tags

setscomplementprime numbersintersectionComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

\(\{1,9,15\}\)

Why is this the correct answer?

The set \(B\) consists of all odd numbers from 1 to 20. The odd prime numbers in this range are 3, 5, 7, 11, 13, 17, and 19. Removing these from B leaves the odd, non-prime numbers \(\{1,9,15\}\). Note that 1 is not prime, because a prime number must have exactly two distinct positive divisors.

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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