3. Among the four statements on real numbers below, how many of them are correct?
"If $a<b$ and $a, b \neq 0$ then $\frac{1}{b}<\frac{1}{a}$ "; "If $a<b$ then $a c<b c$ "; "If $a<b$ then $a+c<b+c$ "; "If $a^{2}<b^{2}$ then $a<b$ ".
(A) 0 ;
(B) 1 ;
(C) 2 ;
(D) 3;
(E) 4 .
3. Ans: (B)
Only the third statement is correct: $a<b$ implies $a+c<b+c$. For other statements, counterexamples can be taken as $a=-1, b=1 ; c=0$ and $a=0, b=-1$ respectively.