Given in a set of real numbers, the relation $R=\{(a,b):a\leq b\}$:

For any $a \in R$, $a \leq a$. Therefore $(a,a) \in R$. Hence $R$ is reflexive.

For any $a \neq b$, we observe that while $a \leq b$ might be true, $b \leq a$ will not be, unless $a=b$.Hence is $R$ is not symmetric.

We can verify this with a simple subsitution:

Let $a = 2, b = 4$. While $a \leq b \rightarrow 2 \leq 4$ is true, $b \leq a \rightarrow 4 \not \leq 2$. Hence $R$ is not symmetric.

For any $(a,b) \in R$, if $a \leq b$ and for any $(b,c) \in R, b \leq c$:

$\Rightarrow a \leq b \leq c \rightarrow a \leq c$.

$\Rightarrow$ If $a \leq c$ then $R$ is transitive.