reflexive relations

Question

Let $R_1, R_2$, relations such that: $R_1 \subseteq R_2$.

If $R_1$ is reflexive then $R_2$ is also reflexive.

I understood it's true, but I don't see why.
if $R_1 \subseteq R_2$ there's $\left\langle {x,x} \right\rangle \in {R_2} \wedge \left\langle {x,x} \right\rangle \notin {R_1}$

Answer 1

Let it be that $R_i$ are relations on set $X$ for $i=1,2$.

Then $(x,x)\in R_1$ is true for every $x\in X$ (definition of reflective relation).

Then $(x,x)\in R_2$ is true for every $x\in X$ since $R_1\subseteq R_2$.

So also $R_2$ appears to be reflective.