Mathematical operation and symbol notation

Mathematical operation and symbol notation

Direction: In the following information question, the symbols @, ©, S, % and are used with the following meaning as illustrated below:
'P © Q' means 'P is either greater than or equal to Q'.
'P % Q' means 'P is either smallest than or equal to Q'.
'P @ Q' means 'P is neither smallest than nor greater to than Q'.
'P S Q' means 'P is smallest than Q'.
'P δ Q' means 'P is greater than Q'.
Now each of the following questions assuming the given statement to be true, find which of the three conclusions I and II given below them is are definitely true.

1. Statements:
J δ D, D @ N, N % F
Conclusions:
I. J δ F II. F © D

1. J > D ...(i) D = N ...(ii) N ≤ F ...(iii)
From (ii) and (iii) D = N ≤ F or F ≥ D ...(iv)
Hence II follows.
From (i) and (iv) R and (iv) J and F can't be compared.
Hence I does not follow.

Correct Option: B

J > D ...(i) D = N ...(ii) N ≤ F ...(iii)
From (ii) and (iii) D = N ≤ F or F ≥ D ...(iv)
Hence II follows.
From (i) and (iv) R and (iv) J and F can't be compared.
Hence I does not follow.

1. Statements:
R S J, J δ F, F % H
Conclusions:
I. H δ J II. R S F

1. R < J ...(i) J > F ...(ii) F ≤ H ...(iii)
From (ii) and (iii) H and J can't be compared.
Hence I does not follow
From (i) and (ii) R and F can't be compared.
Hence II does not follow

Correct Option: D

R < J ...(i) J > F ...(ii) F ≤ H ...(iii)
From (ii) and (iii) H and J can't be compared.
Hence I does not follow
From (i) and (ii) R and F can't be compared.
Hence II does not follow

1. Statements:
B @ N, N © T, T S K
Conclusions:
I. T @ B II. T S B

1. B = N ...(i) N ≥ T ...(ii) T > K ...(iii)
From (i) and (ii) B = N ≥ T or T ≤ B,
Hence I either (T = B) or II (T < B) follows

Correct Option: C

B = N ...(i) N ≥ T ...(ii) T > K ...(iii)
From (i) and (ii) B = N ≥ T or T ≤ B,
Hence I either (T = B) or II (T < B) follows

1. Statements:
H © T, T % M, M δ F
Conclusions:
I. F S T II. H δ M

1. H ≥ T ...(i) T ≤ M ...(ii) M > F ...(iii)
From (i) and (ii) H and M can't be compared. Hence II does not follow
From (ii) and (iii) F and T can't be compared. Hence I does not follow

Correct Option: D

H ≥ T ...(i) T ≤ M ...(ii) M > F ...(iii)
From (i) and (ii) H and M can't be compared. Hence II does not follow
From (ii) and (iii) F and T can't be compared. Hence I does not follow