Arnold F. answered • 02/21/16

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(1) You need to remember the definition of function. f:S -> T is a function if f assigns exactly one element in T for every element in S. Your example of {(1,a), (2,b)} is only one such function. Since you have two elements in S how many ways may they be assigned to elements in B? {(1,a),(2,a)} is another such function.

Can you figure out the rest of this one?

(2) For surjections from T -> S remember all of S must be used e.g. {(a,1),(b,2),(c,1)} works.

How many more are there?

(3) For injections from S -> T two elements in S cannot go to the same element in T; e.g {(1,a),{2.b)} works.

Again how many more are there?

(4) Finally for f from S to T does there exist an inverse function. For f

^{-1 }to exist then f must be both and injection and a surjection. Can you find such an f?Think about these and let me know if you need more help. If so on which part(s).