Mathematics - Functions Question with Solution | TestHub

Case $-\mathbf{I}f(x)\ne 2$ is true, $f(y)=2$ and $f(z)\ne 1$ are false, then $f(x)=1$ or $3,f(y)=1$ or 3 and $f(z)=1$ ⇒ f is not one-one

Case - II $\mathrm{f}(\mathrm{x})\ne 2$ is false, $\mathrm{f}(\mathrm{y})=2$ is true, $\mathrm{f}(\mathrm{z})\ne 1$ is false, then $\mathrm{f}(\mathrm{x})=2,\mathrm{f}(\mathrm{y})=2,\mathrm{f}(\mathrm{z})=1$ ⇒ not possible

Case - III $\mathrm{f}(\mathrm{x})\ne 2$ is false, $\mathrm{f}(\mathrm{y})=2$ is false, $\mathrm{f}(\mathrm{z})\ne 1$ is true, then