The figure shows a system of logic gates. From the study of the truth table, it can be found that to produce a high output $(1)$ at $R$, we must have

$ f: R \rightarrow R $ and $ g:[0, \infty) \rightarrow R $ are defined by $ f(x)=x^{2} $ and $ g(x)=\sqrt{x} $. Which one of the following is not true?

Statement $1$: If the points $(1,2,2), (2,1,2), (2,2,z)$ and $(1,1,1)$ are coplanar,then $z=2$.
Statement $2$: If the $4$ points $P, Q, R$ and $S$ are coplanar,then the volume of the tetrahedron $PQRS$ is $0$.

Particles of masses $m, 2m, 3m, \ldots, nm$ grams are placed on the same line at distances $l, 2l, 3l, \ldots, nl$ $cm$ from a fixed point. The distance of the centre of mass of the particles from the fixed point in centimetres is

Consider two statements $S_1$ and $S_2$.
$S_1$: If $f(x)$ is a differentiable function with $f'(x) = 0$ in $(a, b)$ and $f(x)$ is increasing in $(a, b)$,then $\frac{f(x)}{f'(x)}$ is also increasing in $(a, b)$.
$S_2$: Both $\sin x$ and $\tan x$ are increasing functions in $(0, \frac{\pi}{2})$.
Which of the following is true?