A die has two face each with number ' 1 ', three faces each with number ' 2 ' and one face with number ' 3 '. If the die is rolled once, then $\mathrm{P}(1$ or 3$)$ is
$$ \text { Let } A=\{a, b, c\} \text {, then the number of equivalence relations on A containing }(b, c) \text { is } $$
Let the functions " f " and " g " be $\mathrm{f}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $\mathrm{f}(\mathrm{x})=\sin \mathrm{x}$ and $\mathrm{g}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $g(x)=\cos x$, where $R$ is the set of real numbers
Consider the following statements:
Statement (I): $f$ and $g$ are one-one
Statement (II): $\mathrm{f}+\mathrm{g}$ is one-one
Which of the following is correct?
$$ \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)= $$