Intermediate
Discrete Mathematics & Math
Q73 / 100
How many onto (surjective) functions are there from a 4-element set to a 2-element set?
Correct! Well done.
Incorrect.
The correct answer is B) 14
B
Correct Answer
14
Explanation
Total functions from a 4-set to a 2-set: 2⁴ = 16. Subtract the 2 constant functions (mapping everything to one element), which are not onto: 16 - 2 = 14. This matches the inclusion-exclusion formula for surjections: Σ(-1)^k C(2,k)(2-k)⁴.
Progress
73/100