Let S = {1,2} and T = {a,b,c}. Could you please explain each of theses answers.

Question

Let S = {1,2} and T = {a,b,c}.

Could you please explain each of theses answers.

12. Let S-(1,2) and T = {a,b,c) 14 points (a) How many unique functions are there mapping S T? 2 (b) How many unique functions are there mapping T S? 23-8 (c) How many onto (surjective) functions are there mapping S T? (d) How many onto (surjective) functions are there mapping T S (hint: think of how many non onto functions there are)? (e) How many one-to-one (injective) functions are there mapping S T? (f) How many one-to-one (injective) functions are there mapping T S? (g) Let f : S T, is it possible to define f-17 why or why not? 2 f-1 can be defined only for bijection functions only. However, there is no bijection from ST Thus, 1 cannot be defined.

Explanation / Answer

a) 6+3 = 9

b) 2+6+6 = 14

c) 0

d) 6+6 = 12

e) 0

f) 0

g) no, due to not being a bijective function

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