Thread: Proofs: Domain of composite functions

Here is the question I am trying to solve:

Let R be a relation from A to B and S be a relation from B to C

Prove that: Dom( ) Dom(R)

I imagine that I would begin by trying to prove that:

Dom ( ) Dom(R)

however, I have no idea how to go about doing this. no doubt this stems from my inability to define the domain of a composite function


any help would be much appreciated!

Originally Posted by DHC

Let R be a relation from A to B and S be a relation from B to C, Prove that: Dom(SoR ) Dom(R)

Here is the definition of the composition.
.
From which the proof follows rather easily.

Originally Posted by Plato

Here is the definition of the composition.
.
From which the proof follows rather easily.

how does this sound, then?


{ } { }


hence for x to be in , x must be in Dom(R)