## 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 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:
M % D, D * K, K S N
Conclusions:
I. K © M II. N © D III. M © N

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.

1. Statements:
H © W, W % R, R @ F
Conclusions:
I. R © H II. R @ H

1. H = W ...(i) W ≤ R ...(ii) R > F ...(iii)
From (i) and (ii) H = W ≤ R or R ≥ H, Hence either I (R = H) or II (R > H) follows.

##### Correct Option: C

H = W ...(i) W ≤ R ...(ii) R > F ...(iii)
From (i) and (ii) H = W ≤ R or R ≥ H, Hence either I (R = H) or II (R > H) follows.

1. Statements:
M S T, T @ K, K © D
Conclusions:
I. D S T II. K S M

1. M < T ... (i) T > K ...(ii) K = D ...(iii)
From (ii) and (iii) T > K = D or D < T.
Hence I follow
From (i) and (ii) K and M can't be compared
Hence II does not follow

##### Correct Option: A

M < T ... (i) T > K ...(ii) K = D ...(iii)
From (ii) and (iii) T > K = D or D < T.
Hence I follow
From (i) and (ii) K and M can't be compared
Hence II does not follow

1. Statements:
H @ W, W S M, M # K
Conclusions:
I. K S W II. H @ M

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

##### Correct Option: D

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