Question

Which of the following is/are true?
I. If $xy<0$, then $x>0,y>0$.
II. If $xy>0$, then $x>0,y<0$.
III. If $|x|<5$, then $x\in (-5,5)$.

• A. Only I is true
• B. Only II is true
• C. Only III is true
• D. I and II are true

Answer 1

Answer: (C)

I. If $x>0$ and $y>0$, then $xy>0$ and if $xy<0$, then one of them must less than zero.
II. If $xy>0$, either both are positive or both are negative. i.e., $x>0,y>0$ or $x<0,y<0$
III. $|x|<5$
$\Rightarrow -5<x<5(\because |x|<a\Rightarrow -\beta <x<a)$
$\Rightarrow x\in (-5,5)$