In the following question , the symbols @ , c , $, % and * are used with the following meanings as illustrated below :
'P © Q' means P is not smaller than Q
'P `**` Q' means P is not greater than Q.
'P @ Q' means P is neither greater than nor equal to Q.
'P$ Q' means P is neither smaller than nor equal to Q
'P % Q' means P is neither greater than nor smaller than Q.
Statement : H@B , `B**E` , V©E , W$V.
Conclusion: I.W$E II.H@E III.H@V IV. W$B.

Options

A. only I and II are true
B. only I , II and III are true
C. only II, III and IV are true
D. All are true

Answer

D

Explanation

According to the question
`H @ B implies H lt B " "` …. (i)
`B**E implies B le E " "` …. (ii)
`V © E implies V ge E " "` ….. (iii)
and `W $ V implies W gt V " "` …. (iv)
I.Relation between W and E
From (iv) and (iii) ,we get
`W gt V ge E " "`... (v)
From (v) it is clear that `W gt E`
So, conclusion I i,.e., `W gt E ` is definitely true
II. Relation between H and E
From (i) and (ii) , we get
`H lt B le E " " `.... (vi)
From (vi) , it is clear that `H lt E`
So, conclusion II `i.e, `H lt E` is deinitely true
III. Relation between H and V
From (i) , (ii) and (iii) we get
`H lt B le B le E " "` ... (vii)
From (vii) it is clear that `H lt V`
So, conclusion IV i.e., `W gt B` is definitely true .
Therefore all conclusions are true .