Define$F\left(x\right)$ as the product of two real

functions $f_1\left(x\right)=x,x\in \mathbf{R}$, and $f_2\left(x\right)=\left\{\begin{array}{cll}\sin 1/x& ;& \text{ if }x\ne 0\\ 0& ;& \text{ if }x=0\end{array}\right.$

as follows $\mathrm{F}\left(x\right)=\left\{\begin{array}{ccc}{f}_1\left(x\right)f_2\left(x\right)& ;& x\ne 0\\ 0& ;& x=0\end{array}\right.$

Statement-$1: F\left(x\right)$ is continuous on R

Statement-$2: f1(x$) and $f_2\left(x\right)$ are continuous on$R$.

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
 

 STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1

 STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is False, STATEMENT-2 is True