## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

Direction: In these following question, the symbols @, #,* and % are used with the different meaning as follow:
'A @ B' means 'A is not smallest than B'
'A # B' means 'A is neither smallest than nor equal to B.
'A S B' means 'A is neither than nor smallest than B.
'A * B' means "A is not greater than B'.
'A % B' means 'A is neither greater than or equal to B'
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:
V * W, W S H, H @ I
Conclusions:
I. L * V II. L S D

1. V ≤ W ...(i) W = H ...(ii) H ≥ I ...(iii)
From (i) and (ii) W = H ≥ I or W ≥ I ...(iv)
Hence I ≤ W and II follows But V and I can't be compared From (iii) and (iv)
Hence I does not follows.

##### Correct Option: B

V ≤ W ...(i) W = H ...(ii) H ≥ I ...(iii)
From (i) and (ii) W = H ≥ I or W ≥ I ...(iv)
Hence I ≤ W and II follows But V and I can't be compared From (iii) and (iv)
Hence I does not follows.

1. Statements:
L * P, P % V, V # D
Conclusions:
I. L * V II. L S D

1. L ≤ P.....(i) P < V ...(ii) V > D ...(iii)
Combining (i) and (ii)
we get L ≤ P < V or L < W ...(iv) L and D can't be compared
Hence II does not follows

##### Correct Option: D

L ≤ P.....(i) P < V ...(ii) V > D ...(iii)
Combining (i) and (ii)
we get L ≤ P < V or L < W ...(iv) L and D can't be compared
Hence II does not follows

Direction: In the following information question, the symbols @, #, % and \$ are used with the following meaning as illustrated below:
'P @ Q' means 'P is not smallest than Q'.
'P # Q' means 'P is not greater than Q'.
'P % Q' means 'P is neither greater than nor equal to than Q'.
'P * Q' means 'P is neither smallest than nor greater to than Q'.
'P \$ Q' means 'P is neither smallest than nor greater to than Q'.
Now each of the following questions assuming the given statement to be true, find which of the three conclusions I, II and III given them is are definitely true and give your answer accordingly.

1. Statements:
V @ M, A S M, R # V
Conclusions:
I. R # A II/. V @ A III. R S M

1. V ≥ M ...(i) A > M ...(ii) R ≤ V ...(iii)
These lead us to no relationship by combination.

##### Correct Option: D

V ≥ M ...(i) A > M ...(ii) R ≤ V ...(iii)
These lead us to no relationship by combination.

1. Statements:
T S K, K # R, R * M
Conclusions:
I. M * K II. M % T III. M S K

1. D > K ...(i) K ≤ R ...(ii) R = M ...(iii)
From (ii) and (iii) M ≥ K ...(iv)
Hence either I (M = K) or III (M > K) follow. But M and T can't be compared from (i) and (iv).
Hence II does not follow.

##### Correct Option: B

D > K ...(i) K ≤ R ...(ii) R = M ...(iii)
From (ii) and (iii) M ≥ K ...(iv)
Hence either I (M = K) or III (M > K) follow. But M and T can't be compared from (i) and (iv).
Hence II does not follow.

1. Statements:
B * D, D @ H, H % F
Conclusions:
I. B * F II B S F III. D S F

1. B = D ...(i) D ≥ H ...(ii) H > F ...(iii)
D and F can't be compared from (i) and (ii). And from the same reason, if we bear (i) an mind. B and F can't be compared. Hence none follows.

##### Correct Option: A

B = D ...(i) D ≥ H ...(ii) H > F ...(iii)
D and F can't be compared from (i) and (ii). And from the same reason, if we bear (i) an mind. B and F can't be compared. Hence none follows.