This might seem easy, but im having trouble putting my proofs into words.

Let G = (V,E) be simple graph,

I need to prove for all vertices (x,y,z) of G, the follwoing are true:

1) There is a path from x to x.

2) If there is a path from x to y then there is path y -x.

3)If there is a path from x- y, and y-z then there is path x-z.

Now im not sure whats expected when proofing this.

Do i just say a path from x to x exists since its a path to itself?

and...

if a path x-y exists then there is a path y- x because x and y are two connected vertices by a edge?

and..

if there is a path from x-y, and y-z then there is a path x-z since vertices x and y are connected by an edge, and y-z is connected by an edge, this provides a path from vertices x to z through vertices y.

Id like some feedback if possible thanks.