Question

In the following question, the symbols $\delta$, $\star ,\%,@$ and $\#$ are used with the following meanings as illustrated.
${}^{\prime }A\%B^{\prime }$ means 'A is neither greater than nor equal to B'.
${}^{\prime }A\#B^{\prime }$means 'A is neither smaller than nor equal to B'.
${}^{\prime }A\delta B^{\prime }$ means 'A is neither smaller than nor greater than B'.
${}^{\prime }A\star B^{\prime }$ means 'A is not smaller than B'.
${}^{\prime }A@B^{\prime }$ means 'A is not greater than B'.
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 is/are definitely true and give your answer accordingly.
% $\Rightarrow <$, @ $\Rightarrow$ $\le$ $\#\Rightarrow >$, $\delta$ $\Rightarrow$ =, $\star$ $\Rightarrow$ $\le$
Statements
$P\star D$
$D\#Q$
$Q@R$
Conclusions
I. $Q\%P$
II. $R\#D$
III. $P\#D$

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

Answer 1

The correct option is B Only I is true

Given statements are
P $\star$ D $\Rightarrow$ P $\ge$ D ...(i)
D $\#$ Q $\Rightarrow$ D > Q ...(ii)
Q @ R $\Rightarrow$ Q $\le$ R ...(iii)
After combining these statements, we get
P $\ge$ D > Q $\le$ R
I. Q % P $\Rightarrow$ Q < P (True)
As, P $\ge$ D > Q
So, P > Q
II. R $\#$ D $\Rightarrow$ R > D (False)
As relation cannot be established.
III. P $\#$ D $\Rightarrow$ P > D (False)
As, P $\ge$ D