If D₃ = {x ∈ ℕ : x is prime and 20 < x < 30}, then what is D₃?
Answer and explanation
Correct answer: {23, 29}
The natural numbers strictly between 20 and 30 are 21, 22, 23, 24, 25, 26, 27, 28, and 29. Among them, 23 and 29 are prime: each has exactly two positive divisors, 1 and itself. The other candidates are composite because 21 = 3 × 7, 22 = 2 × 11, 24 is even, 25 = 5 × 5, 26 = 2 × 13, 27 = 3 × 9, and 28 is even. Hence D₃ = {23, 29}.
Frequently asked questions
What is the correct answer to this question?
{23, 29}
Why is this the correct answer?
The natural numbers strictly between 20 and 30 are 21, 22, 23, 24, 25, 26, 27, 28, and 29. Among them, 23 and 29 are prime: each has exactly two positive divisors, 1 and itself. The other candidates are composite because 21 = 3 × 7, 22 = 2 × 11, 24 is even, 25 = 5 × 5, 26 = 2 × 13, 27 = 3 × 9, and 28 is even. Hence D₃ = {23, 29}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
