## 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:
B * K, K © F, F % R
Conclusions:
I. R \$ K II. R \$ B III. F \$ B

1. B ≤ K ...(i) K < F ...(ii) F = W ...(iii)
Combining these we get B ≤ K < F = R
Hence R > K and I follows
Again R > B and II follows.
Also, F > B III follow.

##### Correct Option: B

B ≤ K ...(i) K < F ...(ii) F = W ...(iii)
Combining these we get B ≤ K < F = R
Hence R > K and I follows
Again R > B and II follows.
Also, F > B III follow.

Direction: In the following information question, the symbol %, @, © and are used with the following meaning as illustrated below:
'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 not smallest than Q'.
'P % Q' means 'P is neither smallest than nor greater than Q'.
'P δ Q' means 'P is neither smallest than nor 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:
R © K, K δ M, M *
Conclusions:
I. J δ K II. M @ R III. M % R

1. R ≥ K ...(i) K > M ...(ii) M ≤ J ...(iii)
From (i) and (ii) J and K can't be compared. Hence I does not follow.
From (i) and (ii) R ≥ K > M or K > M or M < R.
Hence II is true but III (M = R) is not.

##### Correct Option: C

R ≥ K ...(i) K > M ...(ii) M ≤ J ...(iii)
From (i) and (ii) J and K can't be compared. Hence I does not follow.
From (i) and (ii) R ≥ K > M or K > M or M < R.
Hence II is true but III (M = R) is not.

1. Statements:
R δ B, B © N, N @ T
Conclusions:
I. N @ R II. T δ B III. T δ R

1. R > B ...(i) B ≥ N ...(ii) N < T ...(iii)
From (i) and (ii) R > B ≥ N or N < R
Hence I is true
From (ii) and (iii) B and T can't be compared.
Hence III does not follow. Nor does III subsequently.

##### Correct Option: B

R > B ...(i) B ≥ N ...(ii) N < T ...(iii)
From (i) and (ii) R > B ≥ N or N < R
Hence I is true
From (ii) and (iii) B and T can't be compared.
Hence III does not follow. Nor does III subsequently.

1. Statements:
W © K, K δ R, R % N
Conclusions:
I. N @ K II. R @ W III. W δ N

1. W ≥ K ...(i) K > R ....(ii) R = N ...(iii)
Combining these we get W ≥ K > R = N
Hence N < K and I follows
Again R < W and II follows.
And, W > N III follows.

##### Correct Option: E

W ≥ K ...(i) K > R ....(ii) R = N ...(iii)
Combining these we get W ≥ K > R = N
Hence N < K and I follows
Again R < W and II follows.
And, W > N III follows.

1. Statements:
H * W, W @ N, N % R
Conclusions:
I. R δ W II. N δ W III. H @ R

1. H ≤ W ..(i) W < N ...(ii) R = N ...(iii)
Combining these we get H ≥ W < N = R
Hence R > W and I follows
Again N > W and II follows
And, H < R III follows

##### Correct Option: D

H ≤ W ..(i) W < N ...(ii) R = N ...(iii)
Combining these we get H ≥ W < N = R
Hence R > W and I follows
Again N > W and II follows
And, H < R III follows