## 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 :
F @ R, R © V, V S T
Conclusion :
I. V % F II. F @ T

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

##### Correct Option: A

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

1. Statement :
N S T, T δ H, N @ W
Conclusion :
I. W % T II. H © N

1. N ≥ T ... (i) T = H ...(ii) N < w .....(iii)
Combining these we get W > N ≥ T = H
Hence W > T and I follows.
Also H ≤ N and II follows

##### Correct Option: E

N ≥ T ... (i) T = H ...(ii) N < w .....(iii)
Combining these we get W > N ≥ T = H
Hence W > T and I follows.
Also H ≤ N and II follows

Direction: In these following question, the symbols @, #,* and % are used with the different meaning as follow:
'A @ B' means 'A is not smallest than B'
'A # B' means 'A is neither smallest than nor equal to B.
'A S B' means 'A is neither than nor smallest than B.
'A * B' means "A is not greater than B'.
'A % B' means 'A is neither greater than or equal to B'
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:
J @ K, K % M, M # T
Conclusions:
I. K % T II. K @ T

1. J ≥ K ...(i) K < M ...(ii) M > T ...(iii)
K and T can't be compared From (ii) and (iii) but either I (K < T) or II, (K ≥ T) must be true.

##### Correct Option: C

J ≥ K ...(i) K < M ...(ii) M > T ...(iii)
K and T can't be compared From (ii) and (iii) but either I (K < T) or II, (K ≥ T) must be true.

1. Statements:
F # R, H % R, L * H
Conclusions:
I. F # L II. R @ L

1. F > R ...(i) H < R ...(ii) L ≤ H ...(iii)
Combining these we get F > R > H ≥ L
Hence F > L and I follows
Also R > L and II (R ≥ L) does not follows.

##### Correct Option: A

F > R ...(i) H < R ...(ii) L ≤ H ...(iii)
Combining these we get F > R > H ≥ L
Hence F > L and I follows
Also R > L and II (R ≥ L) does not follows.

1. Statements:
N @ W, W # H
Conclusions:
I. H % N II. T # W

1. N ≤ W ...(i) W = H ...(ii) H < T ...(iii)
From (i) and (ii) W = N ≥ W > H or N > H ...(iv)
Hence H < N and I follows.
But T and W can't be compared from (ii) and (iii) Hence II does not follow.

##### Correct Option: A

N ≤ W ...(i) W = H ...(ii) H < T ...(iii)
From (i) and (ii) W = N ≥ W > H or N > H ...(iv)
Hence H < N and I follows.
But T and W can't be compared from (ii) and (iii) Hence II does not follow.