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Let A be the set {(n, 2n): n ∈ N} and let B be the set {(2n, 3n): n ∈ N}. What is the intersection A ∩ B?

1. {(n, 6n): n ∈ N}
2. {(2n, 6n): n ∈ N}
3. {(n, 3n): n ∈ N}
4. ∅

Correct answer: ∅

Solution

The sets A and B consist of pairs where the first elements are defined differently, leading to no common pairs. Specifically, the first element of A is n while in B it is 2n, meaning there are no values of n that satisfy both conditions simultaneously.

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