## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

Direction: In these following question, the symbols @, S, #, * and % are used with the different meaning as follow:
'A @ B' means 'A is smallest than B'.
'A S B' means 'A is greater than B'.
'A # B' means 'A is either smallest than or equal to B.
'A * B' means 'A is either greater than or equal to B.
'A % B' means 'A is either smallest than nor greater 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:
V S I, I * M, M # Q
Conclusions:
I. I # Q II. I * Q

1. V > I ...(i) I ≥ M ...(ii) M ≤ Q ...(iii)
From (ii) and (iii) I and Q, can't be compared. But I and II make a complementary pair. Hence either I (I ≤ Q) or II (I ≥ Q) follows.

##### Correct Option: C

V > I ...(i) I ≥ M ...(ii) M ≤ Q ...(iii)
From (ii) and (iii) I and Q, can't be compared. But I and II make a complementary pair. Hence either I (I ≤ Q) or II (I ≥ Q) follows.

1. Statements:
H # T, T @ L, L % F
Conclusions:
I. F S H II. H # L

1. H ≤ T ...(i) T < L ...(ii) L = F ...(iii)
Combining these we get H ≤ T < L = F.
Hence F > H and I follows.
But H < L and Hence II (H ≤ L ) does not follow.

##### Correct Option: A

H ≤ T ...(i) T < L ...(ii) L = F ...(iii)
Combining these we get H ≤ T < L = F.
Hence F > H and I follows.
But H < L and Hence II (H ≤ L ) does not follow.

1. Statements:
H ≥ G < I; F ≤ G > Z
Conclusions:
I. F ≤ H II. Z < I

1. H ≥ G < I; F ≤ G > Z
Check for I:
F ≤ G ≤ H is definitely follows
Check for II:
Z < G < I
∴ Z < I also follows
Hence, both I and II follows

##### Correct Option: E

H ≥ G < I; F ≤ G > Z
Check for I:
F ≤ G ≤ H is definitely follows
Check for II:
Z < G < I
∴ Z < I also follows
Hence, both I and II follows

1. Conclusions:
I. R ≥ S II. W < G

1. S ≤ T < U ≥ W; T ≤ R, G > U
Check for I:
S ≤ T ≤ R
∴ R ≥ S follows
Check for II:
G > U ≥ W
∴ W < G follows
Hence, both I and II follows

##### Correct Option: E

S ≤ T < U ≥ W; T ≤ R, G > U
Check for I:
S ≤ T ≤ R
∴ R ≥ S follows
Check for II:
G > U ≥ W
∴ W < G follows
Hence, both I and II follows

1. Statements:
C ≥ D = E ≤ F; Y < D ≥ W
Conclusions:
I. C ≥ Y II. F ≥ Y

1. C ≥ D = E ≤ F, Y < D ≥ W
Check for I:
C ≥ D > Y
It means C > Y. Thus, I does stand true. check for II:
Y < D ≤ F
It means F > Y. Thus, II also does not stand true.

##### Correct Option: D

C ≥ D = E ≤ F, Y < D ≥ W
Check for I:
C ≥ D > Y
It means C > Y. Thus, I does stand true. check for II:
Y < D ≤ F
It means F > Y. Thus, II also does not stand true.