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Class 10MathematicsSetsSets and their representationsMediumLevel 2

If J = {x : x ∈ ℕ, 10 < x < 20, and both x and 2x + 1 are prime}, then J is:

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Answer and explanation

Correct answer: J = {11}

The natural numbers strictly between 10 and 20 that are prime are 11, 13, 17, and 19. Now test the second condition: for x = 11, 2x + 1 = 23, which is prime; for 13, it is 27, composite; for 17, it is 35, composite; and for 19, it is 39, composite. Hence only x = 11 satisfies both conditions, so J = {11}.

Tags

setsprime numbersset-builder formfinite setsSets and their representationsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

J = {11}

Why is this the correct answer?

The natural numbers strictly between 10 and 20 that are prime are 11, 13, 17, and 19. Now test the second condition: for x = 11, 2x + 1 = 23, which is prime; for 13, it is 27, composite; for 17, it is 35, composite; and for 19, it is 39, composite. Hence only x = 11 satisfies both conditions, so J = {11}.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.

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