Let 
. Then the number of elements in the set 
is onto and 
is
Text Solution
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(1, 1), (1, 4), (4, 1), (2, 4), (4, 2), (3, 4), (4, 3), 
all have one choice for image.
- all have three choices for image
all have two choices for image.
So the total functions 
Case 1 : None of the pre-images have 3 as image
Total functions 
Case 2 : None of the pre-images have 2 as image
Total functions 
Case 3 : None of the pre-images have either 3 or 2 as image
Total functions 
Total onto functions 
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