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 : J $ K , K`**T` , T@N , N © R.
Conclusion : I . J$T II . R `** T` III. N$K , IV. `R**K` .

Options

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

Answer

D

Explanation

According to the question
`J $ K implies J gt K " "` … (i)
`K** T implies K le T " "` …. (ii)
`T @N implies T lt N " "` ….. (iii)
and `N © R implies N ge R " "` …. (iv)
I. Relation between J and T
From (i) and (ii) , we get
`J gt K le T " "` .... (v)
From (v) , we get
`implies` no definite conclusion regarding J and T
So , conclusion I i.e, `J gt T` is not necessarily true .
II. Relation between R and T
From (iii) and (iv) , we get
`T lt N ge R`
From (vi), we get
`implies` no definite conclusion regarding R and T
So, conclusion II i.e, `R le T` is not necessarily true .
III. Relation between N and K
From (ii) and (iii) , we get
`K le T lt N " "` ... (vii)
From (vii) , it is clear that
So, conclusion III i.e, `N gt K` is definitely true
IV. Relation between R and K
From (ii) , (iii) and (iv) , we get
`F le T lt N ge R " "` ..... (viii)
From (viii) , we get
`implies` no definite conclusion regarding R and K .
So, conclusion IV ie . R `le K` is not necessarily true .
Therefore , only conclusion III is definitely true .