If A = {x ∈ N : x is a factor of 30 and x > 30}, what is A?
Answer and explanation
Correct answer: ∅
A natural-number factor of 30 must divide 30 exactly. Every positive factor of a positive integer is less than or equal to that integer; the greatest factor of 30 is 30 itself. The additional condition x > 30 therefore cannot be satisfied by any natural factor of 30. Since no element meets both requirements, the set has no elements and A is the empty set ∅.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
A natural-number factor of 30 must divide 30 exactly. Every positive factor of a positive integer is less than or equal to that integer; the greatest factor of 30 is 30 itself. The additional condition x > 30 therefore cannot be satisfied by any natural factor of 30. Since no element meets both requirements, the set has no elements and A is the empty set ∅.
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.
