Prove that composite relation is function
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Prove that composite relation is function

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    Prove that composite relation is function

    We are given two functions f : A to B and g : B to C. Prove that the composite relation R fog is a function from A to C.

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    Well, the easy part is that a composition fog would be a mapping from A to C. So the real question here is to determine that fog is well-defined. To do this, we have to show that if a = b, then fog(a) = fog(b).

    So, suppose f: A to B and g: B to C are functions. Let a = b be elements of A. Then, since f is a function, and is therefore well-defined, f(a) = f(b). These are elements of B. Since g is a well-defined function from B, g(f(a)) = g(f(b)), elements of C. Hence, fog(a) = fog(b). Therefore, fog is well-defined, and hence, is a function mapping from A to C.

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