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
$H\star W$
$W@N$
$N\%R$
Conclusions
I. $R\delta W$
II. $N\delta W$
III. $H@R$

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

Answer 1

The correct option is D All I, II and III are true

Given statements are
H $\star$ W $\Rightarrow$ H $\le$ W ...(i)
W @ N $\Rightarrow$ W < N ...(ii)
N % R $\Rightarrow$ N = R ...(iii)
After combining these statements, we get H $\le$ W < N = R
R $\delta$ W $\Rightarrow$ R > W is true as N > W.
N $\delta$ W $\Rightarrow$ N > W is also true.
H @ R $\Rightarrow$ H < R is true as H $\le$ W < N.