Question

In the following questions, the symbols @, copyright, pounds ? and $\$$ are used with the following meanings
A @ B means A is neither equal to nor smaller than B.
A copyright B means A is neither greater than nor smaller than B.
A pounds B means A is not equal to B.
A ? B means A is neither greater than nor equal to B.
A $\$$ B means A is either greater or equal to B.
Now, in each of the following questions, assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true.
Statements : J copyright P, P $ N, J pounds H
Conclusions:
I. J copyright N
II. H @ P

• A. If Only Conclusion I is true
  
• B. If Only Conclusion II is true​​​​​​
• C. If Either Conclusion I or 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 D If Neither Conclusion I nor II is true

In these questions, the negative meaning of these symbols is given to establish the relation between A and B, which can be easily converted to its simple and positive meaning. Expressing them mathematically, we get @ $\to$ > (greater than) coppyright $\to$ = (equal to), pounds $\to$ $\ne$ (means either greater than or smaller than, but no definite conclusion), ? $\to$ < (smaller than) and $\$\to \ge$
J = P ....(i)
P $\ge$ N .... (ii)
$J\ne H$ .... (iii)
From Eqs. (i) and (ii), we get $J=P\ge N\Rightarrow J\ge N$
$\Rightarrow$ I may be true but not necessarily so.
From Eqs. (i) and (iii), $P=J\ne H\Rightarrow P\ne H$.
Hence, again II may be true but H , P may be other possibility.
Hence, Ii is not true.