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
U @ N; N $\$$ F; F $\$$ A; A $\square$ R
Conclusions
I. A @ U
II. N $\square$ R
III. R © U
IV. U $\square$ A

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

Answer 1

The correct option is E Only II and either I or IV are true.

Given statements are
U @ N $\Rightarrow$ U = N ...(i)
N $\$$ F $\Rightarrow$ N $\ge$ F ...(ii)
F $\$$ A $\Rightarrow$ F $\ge$ A ...(iii)
A $\square$ R $\Rightarrow$ A > R ...(iv)
Combining all the given statements, we get U = N $\ge$ F $\ge$ A > R
So, A @ U $\Rightarrow$ A = U
N $\square$ R $\Rightarrow$ N > R is true as A > R and N $\ge$ A.
R © U $\Rightarrow$ R $\le$ U is false as U > R.
and U $\square$ A $\Rightarrow$ U > A
So, II is true and either I or IV true.