If A = {x ∈ N : x is a factor of 10} and B = {x ∈ N : x is a factor of 20}, which statement is correct?
Answer and explanation
Correct answer: A ≠ B, but both are finite
The positive natural-number factors of 10 are A = {1, 2, 5, 10}. The positive natural-number factors of 20 are B = {1, 2, 4, 5, 10, 20}. Since 4 and 20 belong to B but not to A, the two sets are not equal. Each fixed positive integer has only finitely many factors, so both sets are finite. Thus option B is the only correct statement.
Frequently asked questions
What is the correct answer to this question?
A ≠ B, but both are finite
Why is this the correct answer?
The positive natural-number factors of 10 are A = {1, 2, 5, 10}. The positive natural-number factors of 20 are B = {1, 2, 4, 5, 10, 20}. Since 4 and 20 belong to B but not to A, the two sets are not equal. Each fixed positive integer has only finitely many factors, so both sets are finite. Thus option B is the only correct statement.
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.
