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