Question

Directions: In the following questions, the symbols @, ©$\$,\ast$ and $\%$ are used with the following meaning as illustrated below.
${}^{\prime }P\copyright Q^{\prime }$ means 'P is smaller than Q'.
${}^{\prime }P@Q^{\prime }$ means 'P is greater than Q'.
${}^{\prime }P\ast Q^{\prime }$ means 'P is either smaller than or equal to Q'.
${}^{\prime }P\%Q^{\prime }$ means 'P is either greater than or equal to Q'.
${}^{\prime }P\$Q^{\prime }$ means 'P is neither smaller than nor greater than Q'.
Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II is/are definitely true?

Statements:
$R\ast B$
$B\copyright D$
$D\$F$
Conclusions:
I. $F@B$
II. $D@R$

• A. Only conclusion I is true
• B. Only conclusion II is true
• C. Either conclusion I or II is true
• D. Neither conclusion I nor II is true
• E. Both conclusions I and II are true

Answer 1

The correct option is E Both conclusions I and II are true

$$\begin{array}{ccc}P\copyright Q\Rightarrow P<Q& P@Q\Rightarrow P>Q& P\ast Q\Rightarrow P\le Q\\ P\%Q\Rightarrow P\ge Q& P\$Q& \end{array}$$
Statements: $R\ast B\Rightarrow R\le B$ © D $\Rightarrow B<D,D\$F\Rightarrow D=F$
So, $R\le B<D=F$
Conclusions:
I. $F@B$ $\Rightarrow F>B$ (True)
II. $D@R$ $\Rightarrow D>R$ (True)
So, both conclusions are true from the given statements.