## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

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

1. Statements:
V © K, K @ B, B S M
Conclusions:
1. None is true
2. Only I is true
3. Only II is true
4. Only III is true
5. Only II and III are true

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

##### Correct Option: C

V < K ...(i) K ≥ B ...(ii) B > M ...(iii)
From (i) and (ii) V and B can't be compared. Hence I does not follow.
From (ii) and (iii) K ≥ B > M or K > M or M < K
Hence II follows.
From (i) and (iv) V and M can't be compared. Hence III does not follow.

1. Statements:
D * R, R % F, F S T
Conclusions:
I. F % D II. F S D III. T © R
1. Only I is true
2. Only II is true
3. Only III is true
4. Only either I or II is true
5. Only either I or II and III are true

1. D ≤ N ...(i) R = F ...(ii) F > T ...(ii)
From (i) and (ii) D ≥ R = F or D ≤ F or F ≥ D.
Hence either I (F = D ) or II (F > D) follows
From (ii) and (iii) R = F > T or R > T or T < R.
Hence III follows.

##### Correct Option: E

D ≤ N ...(i) R = F ...(ii) F > T ...(ii)
From (i) and (ii) D ≥ R = F or D ≤ F or F ≥ D.
Hence either I (F = D ) or II (F > D) follows
From (ii) and (iii) R = F > T or R > T or T < R.
Hence III follows.

1. Statements:
N @ D, D * K, K S A
Conclusions:
I. K @ N II. A © D III. N S A
1. None is true
2. Only I is true
3. Only II is true
4. Only III is true
5. Only II and III are true

1. N ≥ D ...(i) D ≤ N ...(ii) K > A ...(iii)
Obviously none of these in equations can be combined.

##### Correct Option: A

N ≥ D ...(i) D ≤ N ...(ii) K > A ...(iii)
Obviously none of these in equations can be combined.

1. Statements:
K @ T, T S N, N © R
Conclusions:
I. R S K II. N * K III. K S N
1. None is true
2. Only I is true
3. Only II is true
4. Only III is true
5. Only II and III are true

1. N ≥ T ...(i) T > N ...(ii) N < R ...(iii)
From (i) and (ii) N ≥ T. Hence II (N ≤ K) does not follow. From (iii) and (iv) no relationship can be established a between K and R. Hence I does not follow.

##### Correct Option: D

N ≥ T ...(i) T > N ...(ii) N < R ...(iii)
From (i) and (ii) N ≥ T. Hence II (N ≤ K) does not follow. From (iii) and (iv) no relationship can be established a between K and R. Hence I does not follow.

1. Statements:
W % K, K © T, D S F
Conclusions:
I. D S K II. D S W III. F @ W
1. Only I and III are true
2. Only I and II are true
3. Only II and III are true
4. All I, II and III are true
5. None of these

1. W = K ....(i) K < F ...(ii) D > F ...(iii)
Combining these we get W = K < F < D
Hence D > K and I follows
Again D > W and II follows. Also, F > W
Hence III (F ≥ W) does not follow.

##### Correct Option: D

W = K ....(i) K < F ...(ii) D > F ...(iii)
Combining these we get W = K < F < D
Hence D > K and I follows
Again D > W and II follows. Also, F > W
Hence III (F ≥ W) does not follow.