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
D © S; S $\square$ P; P $\$$ I; P @ T
Conclusions
I. P $\#$ D
II. P $\$$ T
III. T $\#$ S
IV. I © D

• A. Only I and III are true
• B. Only III is true
• C. Only III and IV are true
• D. Only II, III and IV are true
• E. Only I, III and IV are true.

Answer 1

The correct option is B Only III is true

Given statements are
D © S $\Rightarrow$ D $\le$ S ...(i)
S $\square$ P $\Rightarrow$ S > P ...(ii)
P $\$$ I $\Rightarrow$ P $\ge$ I ...(iii)
P @ T $\Rightarrow$ P = T ...(iv)
Combining all these statements, we get
D $\le$ S > P = T $\ge$ I. P $\#$ D $\Rightarrow$ P < D is not true as the relation cannot be established.
P $\$$ T $\Rightarrow$ P $\ge$ T is false as P = T
T $\#$ S $\Rightarrow$ T < S is true as S > P = T or S > P.
I © D $\Rightarrow$ I $\le$ D is also false as relation cannot be established. Hence, only conclusion III is true.