If G = {x : x ∈ N, x is a divisor of 18 and x + 1 is prime}, choose the correct roster form of G.
Answer and explanation
Correct answer: G = {1, 2, 6, 18}
To convert the condition into roster form, list the positive divisors of 18: 1, 2, 3, 6, 9, and 18. Check x + 1 for each: 2, 3, 4, 7, 10, and 19. Only 2, 3, 7, and 19 are prime, so the corresponding x-values are 1, 2, 6, and 18. Therefore G = {1, 2, 6, 18}, making option A correct; the other options omit or include unsuitable divisors.
Frequently asked questions
What is the correct answer to this question?
G = {1, 2, 6, 18}
Why is this the correct answer?
To convert the condition into roster form, list the positive divisors of 18: 1, 2, 3, 6, 9, and 18. Check x + 1 for each: 2, 3, 4, 7, 10, and 19. Only 2, 3, 7, and 19 are prime, so the corresponding x-values are 1, 2, 6, and 18. Therefore G = {1, 2, 6, 18}, making option A correct; the other options omit or include unsuitable divisors.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
