Mathematical operation and symbol notation Difficult Questions and Answers

Mathematical operation and symbol notation

Direction: In these question, relationship between different element is shown in the statements. These statements are followed by two conclusions.

Statements:
L ≤ M < N > O ≥ P
Conclusions:
I. O < M II. P ≤ N

If neither conclusion I nor II follows

Correct Option: D

If neither conclusion I nor II follows

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:
K * D, D S L, L @ J
Conclusions:
I. K S L II. K # J

K ≥ D ...(i) D > L ...(ii) L < J ...(iii)
From (i) and (ii) K ≥ D > L or K > L ....(iv)
Hence I follows
However, From (iii) and (iv) J and H can't be compared . Hence II does not follow.

Correct Option: A

K ≥ D ...(i) D > L ...(ii) L < J ...(iii)
From (i) and (ii) K ≥ D > L or K > L ....(iv)
Hence I follows
However, From (iii) and (iv) J and H can't be compared . Hence II does not follow.

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

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:
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.