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Many-One onto Function

Let E = 1, 2,...

Question

Let E = {1, 2, 3, 4} and F {1, 2}. Then the number of onto functions from E to F is

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Solution

The correct option is A 14
The total number of functions are $2^{4} = 16$ . From the total number of functions, subtract those functions which do not have 2 as the range =1. Subtract those functions which do not have 1 as the range.
So, the answer is $16 - 2 = 14$

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