Question

In the following question, $\delta$, $\star$ , %, @ and © are used with the following meaning as illustrated below.
${}^{\prime }P\star Q^{\prime }$ means 'P is not greater than Q'.
${}^{\prime }P@Q^{\prime }$ means 'P is neither greater than nor equal to Q'.
${}^{\prime }P\copyright Q^{\prime }$ means 'P is not smaller than Q'.
${}^{\prime }P\%Q^{\prime }$ means 'P is neither smaller than nor greater than Q'.
${}^{\prime }P\delta Q^{\prime }$ means 'P is neither smaller than nor equal to Q'.
Now, in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given is/are definitely true and give your answer accordingly.
$\star \Rightarrow \le$, @ $\Rightarrow$ >, © $\Rightarrow \le$, % $\Rightarrow$ =, $\delta$ $\Rightarrow$ >
Statements
$R\copyright K$
$K\delta M$
$M\star J$
Conclusions
I. $J\delta K$
II. $M@R$
III. $M\%R$

• A. None of these
• B. Only I is true
• C. Only II is true
• D. Only either II or III is true.
• E. Only III is true

Answer 1

The correct option is C Only II is true

Given statements are
R © K $\Rightarrow$ R $\ge$ K ...(i)
K $\delta$ M $\Rightarrow$ K > M ...(ii)
M $\star$ J $\Rightarrow$ M $\le$ J ...(iii)
After combining all these statements we get $R\ge K>M\le J$
$J\delta K\Rightarrow J>K$ cannot be established.
M @ R $\Rightarrow$ M < R is true as M < K and K $\le$ R.
M % R $\Rightarrow$ M = R is false.