Question

State $T$ for true and $F$ for false.
$\left(i\right)$ If $x<-5$ and $x<-2$, then $x\in \left(-\infty ,-5\right)$
$\left(ii\right)$ If $\left|x\right|\le 4$, then $x\in \left[-4,4\right]$
$\left(iii\right)$ Graph of $x\ge 0$ is

$(iv)$ If $xy>0$, then $x>0$ and $y<0$

	(i)	(ii)	(iii)	(iv)
(a)	$T$	$T$	$T$	$F$
(b)	$T$	$T$	$F$	$T$
(c)	$T$	$F$	$T$	$F$
(d)	$F$	$T$	$T$	$T$

• A. a
• B. b
• C. c
• D. d

Answer 1

Answer: (A)

$(i)$ True
If $x<-5$, then $x\in \left(-\infty ,-5\right)...\left(1\right)$
and $x<-2$, then $x\in \left(-\infty ,-2\right)...\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$, we get $x\in \left(-\infty ,-5\right)$
$\left(ii\right)$ True
If $|x|\le 4$, then $-4\le x\le 4$
$\Rightarrow x\in \left[-4,4\right]$
$\left(iii\right)$ True
The given graph represents $x\ge 0$.
$\left(iv\right)$ False
If $xy>0$, then either $x>0$, $y>0$ or $x<0$, $y<0$.