## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

1. Statements:
B % H, H S E, E @ K
Conclusions:
I. K S H II. K S B III. E © B

1. B = H ...(i) H > E ...(ii) E ≤ K ...(iii)
From (i) and (ii) B = H > E or E < B
Hence III follows.
From (ii) and (iii) H and K can't be compared.
Hence I does not follow. Nor can II follow.

##### Correct Option: B

B = H ...(i) H > E ...(ii) E ≤ K ...(iii)
From (i) and (ii) B = H > E or E < B
Hence III follows.
From (ii) and (iii) H and K can't be compared.
Hence I does not follow. Nor can II follow.

1. Statements:
F @ N, N © D, D @ R
Conclusions:
I. D # F II. R S N III. R S F

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

##### Correct Option: C

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

Direction: In the following information question, the symbol S, %, @, © and are used with the following meaning as illustrated below:
'P % Q' means 'P is smallest than Q'.
'P % Q' means 'P is not greater Q'.
'P * Q' means 'P is neither greater than nor equal to Q'.
'P © Q' means 'P is neither smallest than nor equal to Q'.
'P @ Q' means 'P is neither greater than nor smallest than Q'.

1. Statements:
F S B, B @ H, H % K
Conclusions:
I. B % F II. K @ F II. K S B

1. F ≤ B ...(i) B = H ...(ii) H ≥ K ... (iii)
From (i) B F. Hence I follows.
From (ii) and (iii) B = H ≥ K or B ≥ K or K ≤ B can't be compared. Hence II does not follow.

##### Correct Option: D

F ≤ B ...(i) B = H ...(ii) H ≥ K ... (iii)
From (i) B F. Hence I follows.
From (ii) and (iii) B = H ≥ K or B ≥ K or K ≤ B can't be compared. Hence II does not follow.

1. Statements:
M % D, D * K, K S N
Conclusions:

1. M ≥ D ...(i) D< K ...(ii) K ≤ N ...(iii)
From (i) and (ii) K and M can't be compared.
Hence I does not follow.
From (ii) and (iii) D < K ≤ N or N > D.
Hence II follows. From (i) and II, M and N can't be compared. Hence III does not follow.

##### Correct Option: B

M ≥ D ...(i) D< K ...(ii) K ≤ N ...(iii)
From (i) and (ii) K and M can't be compared.
Hence I does not follow.
From (ii) and (iii) D < K ≤ N or N > D.
Hence II follows. From (i) and II, M and N can't be compared. Hence III does not follow.

Direction: In the following information question, the symbol #, %, @, S and © are used with the following meaning as illustrated below:
'P # Q' means 'P is smallest than Q'.
'P % Q' means 'P is not greater Q'.
'P @ Q' means 'P is neither smallest than nor equal to Q'.
'P S Q' means 'P is neither greater than nor equal to Q'.
'P © Q' means 'P is neither smallest than greater nor greater than Q'.
In each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is are definitely true.

1. Statements:
R % N, N # F, F @ B
Conclusions:
I. F © R II. B S N

1. R ≤ N ...(i) N ≥ F ...(ii) F > B ...(iii)
From (i) and (ii) F and R can't be compared. Hence I does not follow.
Combing (ii) and (iii) we get N ≥ F > B or N > B or B < N. Hence II follows.

##### Correct Option: B

R ≤ N ...(i) N ≥ F ...(ii) F > B ...(iii)
From (i) and (ii) F and R can't be compared. Hence I does not follow.
Combing (ii) and (iii) we get N ≥ F > B or N > B or B < N. Hence II follows.