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If E = {1, 2, 3, 4} and F = {1, 2}, how many onto (surjective) functions are there from E to F?

1. 14
2. 16
3. 12
4. 8

Correct answer: 14

Solution

Total functions from a 4-element set to a 2-element set = 2⁴ = 16. Subtract the 2 functions that are not onto (the constant maps hitting only 1 or only 2). Onto functions = 16 - 2 = 14.

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