Question

In the following questions, the symbols $\#$, $\$$, %, $\star$ and @ are used with the following meaning as illustrated below.
'A $\#$ B' means 'A is not greater than B'.
'A $\$$ B' means 'A is neither smaller than nor equal to B'.
'A % B' means 'A is neither smaller than nor greater than B'.
'A $\star$ B' means 'A is neither greater nor equal to B'.
'A @ B' means 'A is not smaller 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 below them is/are definitely true and give your answer accordingly.
$\#\Rightarrow \le$, @ $\Rightarrow$ $\ge$, $\$$ $\Rightarrow >$, % $\Rightarrow =$, $\star$ $\Rightarrow$ <
Statements
A $\#$ B; B % C; C $\star$ D
Conclusions
I. C @ A
II. A $\#$ D

• A. If only conclusion I is true
• B. If only conclusion II is true
• C. If either conclusion I nor II is true
• D. If neither conclusion I nor II is true
• E. If both conclusions I and II are true.

Answer 1

The correct option is A If only conclusion I is true

Given statements
A $\#$ B $\Rightarrow$ A $\le$ B ...(i)
B % C $\Rightarrow$ B = C ...(ii)
C $\star$ D $\Rightarrow$ C < D ...(iii)
After combining all these statements, we get A $\le$ B = C < D
I. C @ A $\Rightarrow$ C $\ge$ A (True)
As, A $\le$ B = D
So, A $\le$ C
II. A $\#$ D $\Rightarrow$ A $\le$ D (False)
As, A $\le$ B < D
So, A < D