Which set is E = {x ∈ N : x + 2 is a divisor of 10}?
Answer and explanation
Correct answer: E = {3, 8}
The positive divisors of 10 are 1, 2, 5, and 10. Set x + 2 equal to each divisor: x = −1, 0, 3, and 8, respectively. With the usual school convention N = {1, 2, 3, ...}, only 3 and 8 belong to the natural numbers. Hence E = {3, 8}, making option A correct. Option C incorrectly includes 0, and option D lists divisors rather than the corresponding values of x.
Frequently asked questions
What is the correct answer to this question?
E = {3, 8}
Why is this the correct answer?
The positive divisors of 10 are 1, 2, 5, and 10. Set x + 2 equal to each divisor: x = −1, 0, 3, and 8, respectively. With the usual school convention N = {1, 2, 3, ...}, only 3 and 8 belong to the natural numbers. Hence E = {3, 8}, making option A correct. Option C incorrectly includes 0, and option D lists divisors rather than the corresponding values of x.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
