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 : F % W , W © R , R © M , M$D.
Conclusion: I. D@R II.M$F III.R@D IV. `R**F`

Options

A. None is true
B. only III is true
C. only I is true
D. only IV is true

Answer

D

Explanation

According to the question
`F % W implies F = W " "` … (i)
`W © R = W ge R " " `…. (ii)
`R @ M implies R lt M " "` … (iii)
and `M$D implies M gt D " "` …… (iv)
I. Relation between D and R
From (iii) and (iv) , we get
`R lt M gt D " "` ... (v)
From (v) , we get
`implies` no definite conclusion regarding D and R .
So, conclusion I i.e., `D gt R` is not necessarily true
II. Relation between M and F
From (i) , (ii) and (iii) , we get
`F = W ge R lt M " "`... (vi)
From (vi) , we get
`implies ` no definite conclusion regrding M and F .
So, conclusion II i.e, `M gt F` is not necessarily truie .
III. Relation between R and D
From (v) , we get
`implies` no definite conclusion regarding R and D .
So, conclusion III i.e., `R lt D` is not necessarily true .
IV. Relation betwee R and F .
From (i) and (ii) , we get
`F = W ge R " "` ..... (viii)
From (vii) , we get
`R ge F`
So, conclusion IV i.e., `R le F` is definitely true
Therefore ,only cohnclusion IV is definitely true .