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