## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

Direction: In the following information question, the symbols @, ©, %, S and δ are used with the following meaning as illustrated below:
'P % Q' means 'P is greater than Q'
'P δ Q' means 'P is neither greater than smallest than Q'
'P @ Q' means 'P is smallest than Q'.
'p © Q' means 'P is either smallest than or equal to Q'
'P S Q' means 'P is either greater than or equal to 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. Statement :
M @ J, J © R, R δ K
Conclusion :
I. K δ J II. K % J
1. if only conclusion I is true
2. if only conclusion II is true
3. if either conclusion I or conclusion II is true
4. if neither conclusion I nor conclusion II is true
5. if both conclusion I and II are true

1. M < J ...(i) J≤ R ...(ii) R = K .....(iii)
From (ii) and (iii) J ≤ K or K ≥ J, .....(iv)
Hence either I (K = J) or II (K > J) follow

##### Correct Option: C

M < J ...(i) J≤ R ...(ii) R = K .....(iii)
From (ii) and (iii) J ≤ K or K ≥ J, .....(iv)
Hence either I (K = J) or II (K > J) follow

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

1. V > B ...(i) B ≥ D ...(ii) D &Le; E ...(iii)
From (ii) and (iii) E and B can't be compared.
Hence I does not follows. From (i) and (iv) V > D or D < V
Hence II follows

##### Correct Option: A

V > B ...(i) B ≥ D ...(ii) D ≤ E ...(iii)
From (ii) and (iii) E and B can't be compared.
Hence I does not follows. From (i) and (iv) V > D or D < V
Hence II follows

1. Statements: H S N, N % R, R @ J
Conclusions:I. R @ H II. J % H
1. if only conclusion I is true
2. if only conclusion II is true
3. if either conclusion I or conclusion II is true
4. if neither conclusion I nor conclusion II is true
5. if both conclusion I and II are true

1. H ≥ N ....(i) N > R ....(ii) R < J ...(iii)
From (i) and (ii) R > H ...(iv)
Hence R < H and I follows
But J and H can't compared From (iii) and (iv)
Hence II does not follow.

##### Correct Option: A

H ≥ N ....(i) N > R ....(ii) R < J ...(iii)
From (i) and (ii) R > H ...(iv)
Hence R < H and I follows
But J and H can't compared From (iii) and (iv)
Hence II does not follow.

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

1. F = T ....(i) T ≥ M ....(ii) M ≤ R .....(iii)
From (i) and (ii) F ≥ M ....(iv)
Hence M ≤ F and II follows
But R and F can't be compared From (iii) and (iv)
Hence I does not follow

##### Correct Option: B

F = T ....(i) T ≥ M ....(ii) M ≤ R .....(iii)
From (i) and (ii) F ≥ M ....(iv)
Hence M ≤ F and II follows
But R and F can't be compared From (iii) and (iv)
Hence I does not follow

1. Statement :
W © D, D S B, B @ H
Conclusion :
I. H % D II. W @ B
1. if only conclusion I is true
2. if only conclusion II is true
3. if either conclusion I or conclusion II is true
4. if neither conclusion I nor conclusion II is true
5. if both conclusion I and II are true

1. W ≤ D ....(i) D ≥ B .....(ii) B > H ... (iii)
H and D can't be compared from (ii) and (iii)
Hence; I does not follows
Nor can W and B he be compared From (i) and (ii).
Hence II does not follows

##### Correct Option: D

W ≤ D ....(i) D ≥ B .....(ii) B > H ... (iii)
H and D can't be compared from (ii) and (iii)
Hence; I does not follows
Nor can W and B he be compared From (i) and (ii).
Hence II does not follows