Question

Which of the following is/are true?
I. If $x y<0$, then $x>0, y>0$.
II. If $x y>0$, 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 $x y > 0$ and if $x y< 0$, then one of them must less than zero.
II. If $x y >0$, 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) $