Question

Given below are pairs of statements. In each case, combine them using 'if and only if'.

(i) p: In $\Delta ABC,\angle B=\angle C.$

q: In $\Delta ABC,AC=AB.$

(ii) p: A and B are two sets such that $A\subseteq B$ and $B\subseteq A.$

q: $A=B.$

(iii) p: $\Delta ABC$ is equilateral.

q: $\Delta ABC$ is equiangular.

(iv) p: $\{a\in Rsuchthat\left|a\right|<2\}.$

q: $\{a\in Rsuchthat(a>-2anda<2\left)\right\}.$

Answer 1

We can combine the given statements as given below.

(i) $\Delta ABC,\angle B=\angle C\iff AC=AB.$

(ii) For any sets A and B, $A=B\iff (A\subseteq BandB\subseteq A).$

(iii) A $\Delta ABC$ is equilateral $\iff$ it is equiangular.

(iv) For every real $a,|a|<2\iff (a>-2anda<2).$