# Thread: Really easy proof just don't know where to start

1. ## Really easy proof just don't know where to start

I got a really easy proof that i know are true but i'm really bad about proving things just need a little help getting started

suppose f:A->B and g:B->C show that g0f is a constant function if either f or g is constant

it is really easy to see that this is true by def but not sure how to formally prove this

2. Originally Posted by action259
I got a really easy proof that i know are true but i'm really bad about proving things just need a little help getting started

suppose f:A->B and g:B->C show that g0f is a constant function if either f or g is constant

it is really easy to see that this is true by def but not sure how to formally prove this
We are mapping two non-empty sets by,
$\displaystyle f:A\to B$ such that,
$\displaystyle f(x)=b\in B \, \forall x\in A$
Let,
$\displaystyle g:B\to C$ be any function between two non-empty sets B and C,
Then,
$\displaystyle g \circ f:A\to C$
Is a map between these two sets.
It is,
$\displaystyle g(f(x))=g(b)\forall x\in A$
Thus, it is konstant.

Similary argument in the other direction.