If X₁ = {x : x ∈ ℕ, x is a divisor of 42, and x > 6}, what is the roster form of X₁?
Answer and explanation
Correct answer: X₁ = {7, 14, 21, 42} — X₁ = {7, 14, 21, 42}
The positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The condition x > 6 excludes 1, 2, 3, and 6 because they are not greater than 6. The remaining divisors are therefore 7, 14, 21, and 42. Hence the roster form is X₁ = {7, 14, 21, 42}, making option A correct. Notice that 6 is excluded because the inequality is strict, not x ≥ 6.
Frequently asked questions
What is the correct answer to this question?
X₁ = {7, 14, 21, 42} — X₁ = {7, 14, 21, 42}
Why is this the correct answer?
The positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The condition x > 6 excludes 1, 2, 3, and 6 because they are not greater than 6. The remaining divisors are therefore 7, 14, 21, and 42. Hence the roster form is X₁ = {7, 14, 21, 42}, making option A correct. Notice that 6 is excluded because the inequality is strict, not x ≥ 6.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
