Show that the relation $\mathrm{R}$ on $\mathit{ℝ}$ defined as $\mathrm{R}=\left\{\left(\mathrm{a},\mathrm{b}\right):\mathrm{a}\le \mathrm{b}\right\}$, is reflexive, and transitive but not symmetric.
OR
Prove that the function $\mathrm{f}:\mathrm{N}⟶\mathrm{N}$, defined by $\mathrm{f}\left(\mathit{x}\right)={\mathit{x}}^2+\mathit{x}+1$ is one-one but not onto. Find inverse of $\mathit{f}:\mathit{N}⟶\mathit{S}$, where $\mathit{S}$ is range of $\mathit{f}$.