## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

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

1. Statements:
I # N
Conclusions:
I. J % T II. T S N III. N @ J
1. None follow
2. Only I and II follow
3. Only I and III follow
4. Only II and III follow
5. All follow

1. J ≤ N ...(i) K ≤ N ...(ii) T > K ...(iii)
Combining these we get T > K ≥ N ≥ J
Hence J < T and I follows. Also T > N and II follows.
Beside N ≥ J and III follows

##### Correct Option: E

J ≤ N ...(i) K ≤ N ...(ii) T > K ...(iii)
Combining these we get T > K ≥ N ≥ J
Hence J < T and I follows. Also T > N and II follows.
Beside N ≥ J and III follows

1. Statements:
M % R, R # T, T * N
Conclusions:
I. N * R, II. NSR, II. NSM
1. All follow
2. Only either I or II follows
3. Only either I or II and III follow
4. Only either I or III and II follow
5. None of these

1. M < R ...(i) R ≤ T ...(ii) T = N ...(iii)
Combining these we get M < R ≤ T = N
Hence N ≤ R
Which means either I (N = R) or II (N > R) follows.
Again N > M. Hence III follows

##### Correct Option: C

M < R ...(i) R ≤ T ...(ii) T = N ...(iii)
Combining these we get M < R ≤ T = N
Hence N ≤ R
Which means either I (N = R) or II (N > R) follows.
Again N > M. Hence III follows

Direction: In the following information question, the symbols @, ©, S, % and are used with the following meaning as illustrated below:
'P © Q' means 'P is either greater than or equal to Q'.
'P % Q' means 'P is either smallest than or equal to Q'.
'P @ Q' means 'P is neither smallest than nor greater to than Q'.
'P S Q' means 'P is smallest than Q'.
'P δ Q' means 'P is greater than Q'.
Now each of the following questions assuming the given statement to be true, find which of the three conclusions I and II given below them is are definitely true.

1. Statements:
M % R, R S T, T © K
Conclusions:
I. T δ M II. R S T
1. if only conclusion I is true
2. if only conclusion II is true
3. if either conclusion I or II is true
4. if neither conclusion I nor II is true
5. if both conclusion I and II are true

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

##### Correct Option: A

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

1. Statements:
W % V, V @ Z, Z © D
Conclusions:
I. D % V II. W % Z
1. if only conclusion I is true
2. if only conclusion II is true
3. if either conclusion I or II is true
4. if neither conclusion I nor II is true
5. if both conclusion I and II are true

1. W ≤ V ..(i) V = Z ...(ii) Z ≥ D ...(iii)
From (ii) and (iii) V = Z ≥ D or D ≤ V
Hence I follows.
From (i) and (ii) W ≤ V = Z or W ≤ Z
Hence II follows.

##### Correct Option: E

W ≤ V ..(i) V = Z ...(ii) Z ≥ D ...(iii)
From (ii) and (iii) V = Z ≥ D or D ≤ V
Hence I follows.
From (i) and (ii) W ≤ V = Z or W ≤ Z
Hence II follows.

1. Statements:
B δ T, T S H, H @ M
Conclusions:
I. M δ T II. B δ H
1. if only conclusion I is true
2. if only conclusion II is true
3. if either conclusion I or II is true
4. if neither conclusion I nor II is true
5. if both conclusion I and II are true

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

##### Correct Option: A

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