If G = {x ∈ ℕ : x is a prime divisor of 42}, what is G?
Answer and explanation
Correct answer: G = {2, 3, 7}
To find G, first list the positive divisors of 42: 1, 2, 3, 6, 7, 14, 21, and 42. From this list, identify the numbers that are prime. The numbers 2, 3, and 7 are prime because each has exactly two positive factors, 1 and itself. The number 1 is neither prime nor composite, while 6, 14, 21, and 42 are composite. Therefore, the set of prime divisors of 42 is G = {2, 3, 7}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
G = {2, 3, 7}
Why is this the correct answer?
To find G, first list the positive divisors of 42: 1, 2, 3, 6, 7, 14, 21, and 42. From this list, identify the numbers that are prime. The numbers 2, 3, and 7 are prime because each has exactly two positive factors, 1 and itself. The number 1 is neither prime nor composite, while 6, 14, 21, and 42 are composite. Therefore, the set of prime divisors of 42 is G = {2, 3, 7}, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
