Total Relation

Left Total Relation

A Binary Relation $\{(x,y)\},x\in X,y\in Y$ is left total if $\forall x\in X,\exists y\in Y\text{ s.t }xRy$

Right Total Relation

A Binary Relation $\{(x,y)\},x\in X,y\in Y$ is left total if $\forall y\in Y,\exists x\in X\text{ s.t }xRy$