If A = {x ∈ ℕ : x is a factor of 30 and x is prime}, then which set is A?
Answer and explanation
Correct answer: A = {2, 3, 5};
The positive factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Among these factors, the prime numbers are 2, 3, and 5 because each has exactly two positive divisors: 1 and itself. The number 1 is not prime, and 30 is composite because it has more than two positive divisors. Hence the required set in roster form is A = {2, 3, 5}.
Frequently asked questions
What is the correct answer to this question?
A = {2, 3, 5};
Why is this the correct answer?
The positive factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Among these factors, the prime numbers are 2, 3, and 5 because each has exactly two positive divisors: 1 and itself. The number 1 is not prime, and 30 is composite because it has more than two positive divisors. Hence the required set in roster form is A = {2, 3, 5}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
