Mathematical operation and symbol notation Difficult Questions and Answers

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.

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

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.

Statements:
V S I, I * M, M # Q
Conclusions:
I. I # Q II. I * Q

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.

Statements:
P @ W, W * D, D S J
Conclusions:
I. J @ P II. J @ W

P < W ...(i) W ≥ D ...(ii) D > J ...(iii)
From (ii) and (iii) W ≥ D > J or J < W ...(iv)
Hence II follows. However, from (i) and (iv) we can conclude that J and P can't be compared. Hence I does not follow.

Correct Option: B

Statements:
E @ U, U %R, R S F
Conclusions:
I. E S F II. E * F

E < U ...(i) U = R ...(ii) R > F ...(iii)
From (i) and (ii) E < R ...(iv)
Now, From (iii) and (iv) E and F can't be compared
Hence neither I nor II follows.

Correct Option: D

E < U ...(i) U = R ...(ii) R > F ...(iii)
From (i) and (ii) E < R ...(iv)
Now, From (iii) and (iv) E and F can't be compared
Hence neither I nor II follows.

Statements:
T # J, J * I, I @ W
Conclusions:
I. J @ W II. T % I

T ≤ J ...(i) J ≥ I ...(ii) I < W ...(iii)
From (ii) and (iii) J and W can't be compared. Hence I does not follow
From (i) and (ii) T and I can't be compared. Hence II does not follow

Correct Option: D

T ≤ J ...(i) J ≥ I ...(ii) I < W ...(iii)
From (ii) and (iii) J and W can't be compared. Hence I does not follow
From (i) and (ii) T and I can't be compared. Hence II does not follow