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If a set A has 3 elements and a set B has 2 elements, how many non-empty relations can be defined from A to B?

1. 63
2. 31
3. 7
4. 15

Correct answer: 63

Solution

Each relation is a subset of A x B, which has n(A)*n(B) ordered pairs. The total number of subsets is 2 raised to that count; removing the empty set gives the non-empty relations.

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