## 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. 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. 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. None is true
2. Only I is true
3. Only II is true
4. Only either II and III are true
5. Only III is true

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. 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. 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. Only I and II are true
2. Only either II or III is true
3. Only II and III are true
4. Only I and III are true
5. All I, II and III are true

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. Only I and II are true
2. Only II and III are true
3. Only I and III are true
4. All I, II and III are true
5. None of these

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