## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

Direction: In the following information question, the symbol %, @, © and are used with the following meaning as illustrated below:
'P * Q' means 'P is not greater than Q'.
'P @ Q' means 'P is neither greater than nor equal to than Q'.
'P © Q' means 'P is not smallest than Q'.
'P % Q' means 'P is neither smallest than nor greater than Q'.
'P δ Q' means 'P is neither smallest than nor than Q'.
Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true and give your answer accordingly.

1. Statements:
Z % M, M * F, F δ D
Conclusions:
I. F % Z II. F δ Z III. D @ Z
1. Only I is true
2. Only either I or II is true
3. Only II is true
4. Only III is true
5. None of these

1. Z = M ...(i) M ≤ F ...(ii) F > D ...(iii)
From (i) and (ii) Z = M ≤ F or F ≥ Z ...(iv)
Hence either F = Z (I is true) or F > Z (II follows)
From (iii) and (iv) no relationship can be established between D and Z Hence III does not follow.

##### Correct Option: B

Z = M ...(i) M ≤ F ...(ii) F > D ...(iii)
From (i) and (ii) Z = M ≤ F or F ≥ Z ...(iv)
Hence either F = Z (I is true) or F > Z (II follows)
From (iii) and (iv) no relationship can be established between D and Z Hence III does not follow.

1. Statements:
D @ K, K % F, F © B
Conclusions:
I. F δ D II. B @ K III. B % K
1. Only I is true
2. Only II is true
3. Only III is true
4. Only either II or III is true
5. Only either II or III and I are true

1. D < K ...(i) K = F ...(ii) F ≥ B ...(iii)
From (i) and (ii) D < K = F or F > D
Hence I is true
From (ii) and (iii) K = F ≥ B or B ≤ K. Hence either II
(B < K) or (B = K) is true

##### Correct Option: E

D < K ...(i) K = F ...(ii) F ≥ B ...(iii)
From (i) and (ii) D < K = F or F > D
Hence I is true
From (ii) and (iii) K = F ≥ B or B ≤ K. Hence either II
(B < K) or (B = K) is true