Consider two sets $$A = \left\{2, 3, 5, 7, 11, 13 \right\}$$ and $$B = \left\{1, 8, 27 \right\}$$. Let f be a

Question

Consider two sets $$A = \left\{2, 3, 5, 7, 11, 13 \right\}$$ and $$B = \left\{1, 8, 27 \right\}$$. Let f be a function from A to B such that for every element in B, there is at least one element a in A such that $$f(a) = b$$. Then, the total number of such functions f is

Accepted Answer

540. Set A={2,3,5,7,11,13} so |A|=6 Set B={1, 8, 27} so |B|=3 Without any restrictions, each element in A can map to any of the 3 elements in B. Thus, the total number of functions is: 3 6 = 729 3^6=729 3 6 = 729 Excluding Functions That Miss One Element in B: If a function does not map to an element in

Consider two sets $A = \left\{2, 3, 5, 7, 11, 13 \right\}$ and $B = \left\{1, 8, 27 \right\}$ . Let f be a function from A to B such that for every element in B, there is at least one element a in A such that $f(a) = b$ . Then, the total number of such functions f is

Consider two sets $A = \left\{2, 3, 5, 7, 11, 13 \right\}$ and $B = \left\{1, 8, 27 \right\}$ . Let f be a function from A to B such that for every element in B, there is at least one element a in A such that $f(a) = b$ . Then, the total number of such functions f is