Solution to Let A = {a,b,c,d}, B = {1,2,3}, and R = {(a,2), (b, 1), (c, 2), … - Sikademy
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Archangel Macsika

Let A = {a,b,c,d}, B = {1,2,3}, and R = {(a,2), (b, 1), (c, 2), (d, 1)}. (a)Is R a function? (b)Is R−1 a function? Explain your answers.

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(a) A function f from A to B is an assignment of exactly one element of B to each element of A.

Yes, R is a function: for each input there is exactly one output. 


(b) R^{-1} is not a function. For example, b \not= d, but f^{-1}(1)=b, f^{-1}(1)=d

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