Question

Directions: In the following questions, the symbols @ copyright $\%\$$ and $\ast$ are used with the following meaning as illustrated.
'P copyright Q' means 'P is not greater than Q'.
${}^{\prime }P\ast Q^{\prime }$ means 'P is not smaller than Q'.
${}^{\prime }P\%Q^{\prime }$ means 'P is neither greater than nor equal to Q'.
${}^{\prime }P\$Q^{\prime }$ means 'P is neither smaller than nor equal to Q'.
'P @ Q' means 'P is neither greater than nor smaller than Q'.
Now in each of the following questions assuming the given statements to be true, find out which of the three conclusions I, II and III given below them is/are definitely true.
Statements: $B\%H,H\$J,J\ast M$
Conclusions:
I. $B\%J$
II. $M\%B$
III. $H\$M$

• A. None is true
• B. Only I is true
• C. Only II is true
• D. Only III is true
• E. Only II and III are true

Answer 1

The correct option is D Only III is true

$\begin{array}{cc}copyright\to \le & \$\to >\\ \ast \to \ge & @\Rightarrow =\\ \%\to <& \end{array}$
Statements: $B\%H\Rightarrow B<H$,
$H\$J\Rightarrow H>J$,
$J\ast M\Rightarrow J\ge M$
$\therefore B<H>J\ge M$
Conclusions:
I. $B\%J\Rightarrow B<J$ (False)
II. $M\%B\Rightarrow M<B$ (False)
III. $H\$M\Rightarrow H>M$ (True)
Only III is true.