What kind of set is A = {x : x ∈ ℕ, x is a factor of 18, and x > 18}?
Answer and explanation
Correct answer: Empty set
Every positive factor of 18 is at most 18. Its natural-number factors are 1, 2, 3, 6, 9, and 18; none is greater than 18. Consequently, no natural number can satisfy both conditions “x is a factor of 18” and “x > 18.” A set with no element satisfying its defining condition is the empty set, so A = ∅.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
Every positive factor of 18 is at most 18. Its natural-number factors are 1, 2, 3, 6, 9, and 18; none is greater than 18. Consequently, no natural number can satisfy both conditions “x is a factor of 18” and “x > 18.” A set with no element satisfying its defining condition is the empty set, so A = ∅.
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.
