## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

1. Statements:
W @ F, F S M, M © D
Conclusions:
I. D S F II. W © B III. F S D

1. W ≥ F ...(i) F > M ...(ii) M < D ...(iii)
From (i) and (ii) W and M can't be compared. Hence II does not follow.
From (ii) and (iii) F and D can't be compared. Hence neither I or III follows.

##### Correct Option: A

W ≥ F ...(i) F > M ...(ii) M < D ...(iii)
From (i) and (ii) W and M can't be compared. Hence II does not follow.
From (ii) and (iii) F and D can't be compared. Hence neither I or III follows.

1. Statements:
M # W, W % N, N S B
Conclusions:
I. N % M II. N © M III. M S B

1. M ≥ W ...(i) W = N ...(ii) N > B ...(iii)
Combining these we get M ≥ W = N > B.
Hence M ≥ N or N ≤ M,
Which means either I (N = M) or II (N < M) follows.
Also M > B and II (M ≤ D) Hence III deficitely true.

##### Correct Option: C

M ≥ W ...(i) W = N ...(ii) N > B ...(iii)
Combining these we get M ≥ W = N > B.
Hence M ≥ N or N ≤ M,
Which means either I (N = M) or II (N < M) follows.
Also M > B and II (M ≤ D) Hence III deficitely true.

Direction: In these following question, the symbols @, S, #, * and % are used with the different meaning as follow:
'A @ B' means 'A is smallest than B'.
'A S B' means 'A is greater than B'.
'A # B' means 'A is either smallest than or equal to B.
'A * B' means 'A is either greater than or equal to B.
'A % B' means 'A is either smallest than nor greater 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:
P @ W, W * D, D S J
Conclusions:
I. J @ P II. J @ W

1. P < W ...(i) W ≥ D ...(ii) D > J ...(iii)
From (ii) and (iii) W ≥ D > J or J < W ...(iv)
Hence II follows. However, from (i) and (iv) we can conclude that J and P can't be compared. Hence I does not follow.

##### Correct Option: B

P < W ...(i) W ≥ D ...(ii) D > J ...(iii)
From (ii) and (iii) W ≥ D > J or J < W ...(iv)
Hence II follows. However, from (i) and (iv) we can conclude that J and P can't be compared. Hence I does not follow.

1. Statements:
H # T, T @ L, L % F
Conclusions:
I. F S H II. H # L

1. H ≤ T ...(i) T < L ...(ii) L = F ...(iii)
Combining these we get H ≤ T < L = F.
Hence F > H and I follows.
But H < L and Hence II (H ≤ L ) does not follow.

##### Correct Option: A

H ≤ T ...(i) T < L ...(ii) L = F ...(iii)
Combining these we get H ≤ T < L = F.
Hence F > H and I follows.
But H < L and Hence II (H ≤ L ) does not follow.

1. Statements:
V S I, I * M, M # Q
Conclusions:
I. I # Q II. I * Q

1. V > I ...(i) I ≥ M ...(ii) M ≤ Q ...(iii)
From (ii) and (iii) I and Q, can't be compared. But I and II make a complementary pair. Hence either I (I ≤ Q) or II (I ≥ Q) follows.

##### Correct Option: C

V > I ...(i) I ≥ M ...(ii) M ≤ Q ...(iii)
From (ii) and (iii) I and Q, can't be compared. But I and II make a complementary pair. Hence either I (I ≤ Q) or II (I ≥ Q) follows.