Question

[Discrete math/equivalence relations:] R is a reflexive relation on X, such that for all x, y, z in X, if xRy and yRz, then zRx. Prove that R is an equivalence relation.

The symmetry part of the proof in the textbook I don't understand. It says,

Suppose that xRy. Since R is reflexive, yRy. Taking z = y in the given condition, we have yRx. Therefore R is symmetric.

Questions to come.

Answer 1

Reflexive is what

Answer 2

Reflexive means for every x in X there exists (x,x) in R.

Answer 3

How come z=y? And where's the other half of the condition in there? the yRz? Because it's if xRy AND yRz then zRx... so... lost

Answer 4

@ganeshie8 @loser66 @wio

Answer 5

what is this xRy and yRy mean?

Answer 6

Are you still here?

Answer 7

xRy, of coursse, yRx. It likes a couple (hahahaha) if a girl Loves a man, then the man Loves the girl in "couple field"
Now, xRy, hence y R x
but y R z also, then z must be x since we have "couple" relationship only, not "triple"