1. ## relation question

let R be a relation on real numbers that is symmetric and transitive.
prove that if Dom(R) = real numbers then R is reflexive.

Can someone help me out with this please?

2. ## Re: relation question

Hint: Can you make two steps and come to your initial position?

Of course, real numbers are irrelevant here. What matters is that for every $x$ there exists a $y$ such that $xRy$, i.e., $\operatorname{dom} R$ is the whole set on which $R$ is defined.

3. ## Re: relation question

Proof:
Let R be a relation on R that is symmetric and transitive.
Suppose Dom(R) = R.
Consider real number x.
Since x is in Dom(R) = R, there exists y in R such that xRy.
Since R is symmetric, yRx.
Since R is transitive, xRx.
Thus, for all x in R, xRx.

Therefore, R is reflexive.