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 : `K**D` , D$N , N%M , M© W.
Conclusion : M@K II N@K III M@D IV `W**N`

Options

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

Answer

B

Explanation

According to the question
`K ** D implies K le D " "` … (i)
`D $ D implies D gt N " "` …. (ii)
`N % M implies N = M " "` … (iii)
and `M © W implies M ge W " "` … (iv)
I. Relation between M and K
From (i) , (ii) and (iii) , we get
`K le D gt N = M " "` ... (v)
From (v) , we get
`implies` No definite conclusion regarding M and K
So , conclusion I
i.e, `M @K implies M lt K` is not necessarily true
II. Relation between N and K
From (i) and (ii) , we get
`K le D gt N " "` ... (vi)
From (vi) , we get
`implies` No definite conclusion regarding N and K
So, conclusion II
i.e, `N @ K implies N lt K` is necessarily true
III. Relation between M and D
From (ii) and (iii) , we get
`D gt N = M " "` .. (vii)
From (vii) , it is clear that
`M lt D`
So, conclusion III
i.e, `M @ D implies M lt D `is definitely true
IV. Relation between W and N
From (iii) and (iv) , we get
`N = M ge W " "` ..... (viii)
From (viii) , it is clear that `W le N`
So, conclusion IV
i.e, `W ** N implies W le N` is definitely true .
So , only conclusion III and IV are definitely true