To find $R\circ R^{-1}$ in Discrete mathematics Today I came across a question in DMS which says:

If $R$ is the relation “Less Than” from $A = \{1, 2, 3, 4\}$ to $B = \{1,3,5\}$ then find $R\circ R^{-1}$.

Now what is $R\circ R^{-1}$?
I know how to find $R\circ R$, 
like in this question firstly we will find $R$ where 
$$R= \{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}$$
and then $R\circ R$ would be:
$$\{(1,5),(2,5),(3,5),(4,5)\}.$$
Please correct me if I'm wrong.
And also please explain how to find $R\circ  R^{- 1}$?
Thanks in advance :-) 

If $R\subseteq A\times B$, $S\subseteq B\times C$ are relations, then $S\circ R\subset A\times C$ is given by $$S\circ R=\{\,(a,c)\mid\exists b\in B\colon aRb\land bRc\,\}. $$
(So as a side remark, your example calculation of an $R\circ R$ is wrong, cf. Nils Ziehn's comment).
Moreover $R^{-1}\subseteq B\times A$ is the reverse relation, given by
$$ R^{-1}=\{\,(b,a)\mid aRb\,\}.$$
Putting these togeher, $R\circ R^{-1}$ is a relation $\subseteq B\times B$ and specifically
$$R\circ R^{-1}=\{\,(b_1,b_2)\mid\exists a\in A\colon a<b_1\land a<b_2\,\}. $$
Can you write that down explicitly?
