Question

In the following questions, the symbols ©, $\#$, @,
$\square$ and $\$$ are used with the following meaning as illustrated below.
'P ©Q' means 'P is not greater than Q'.
'P $\#$ Q' means 'P is neither greater than nor equal to Q'.
'P @ Q' means 'P is neither greater than nor smaller than Q'.
'P $\square$ Q' means 'P is neither smaller than nor equal to Q'
'P $\$$ Q' means 'P is not smaller than Q'.
Now, in each of the following questions assuming the given statements to be true, find which of the conclusions given below them are definitely true.
$\copyright \Rightarrow \le$ $\#$ $\Rightarrow <$ @ $\Rightarrow$ = $\square \Rightarrow >$ $\$$ $\Rightarrow \ge$

Statements
$A\square N$; S $\$$ N; S $\square$ W; W © R
Conclusions
I. R $\$$ A
II. S $\square R$
III. S $\square$ A
IV. W © A

• A. Only I and II are true
• B. Only II, III and IV are true
• C. None is true
• D. All I, II, III and IV are true.
• E. None of the above.

Answer 1

The correct option is C None is true

Statements are
$A\square N$ $\Rightarrow A>N$ ...(i)
S $\$$ N $\Rightarrow S\ge N$ ...(ii)
$S\square W$ $\Rightarrow S>W$ ...(iii)
$W\copyright R$ $\Rightarrow W\le R$ ...(iv)
Combining all the statements, we get,
$A>N\le S>W\le R$, so R $\$$ A $\Rightarrow R\ge A$ is
not true as relation cannot be established.
$S\square R\Rightarrow S>R$ is also not true.
$S\square A\Rightarrow S>A$ is also not true.
$W\copyright R\Rightarrow W\le A$ is also not true.
No relation can be established.