## Mathematical operation and symbol notation

#### Mathematical operation and symbol notation

Direction: In the following questions, the symbols δ, \$, , @ and © are used with the meaning as indicated below.
'P \$ Q' means 'P is neither equal to nor greater than Q'.
'P © Q' means 'P is neither equal to nor smaller than Q'
'P δ Q' means 'P is neither greater than nor smaller to Q'.
'P @ Q' means 'P is not smaller than Q'.
'P ∗ Q' means 'P is not greater than Q'.

in each question, three statements showing relationship, have been given , which are followed by three Conclusions I, II and III. Assuming that the given statements to be true, find out which conclusion(s) is/are definitely true.

1. Statements
B © N, N @ R, F ∗ R
Conclusions
II. F ∗ N
III. R \$ B
1. I and II are true
2. I and III are true
3. II and III are true
4. I, II and III are true
5. None of the above

1. Statements
B © N ⇒ B > N,
N @ R ⇒ N ≥ R, F H R ⇒ F ≤ R
So, B > N ≥ R ≥ F
Conclusions
I. B © R ⇒ B > R      ( true)
II. F H N ⇒ F ≤ N       (true)
III. R \$ B ⇒ R < B       (true)

##### Correct Option: D

Statements
B © N ⇒ B > N,
N @ R ⇒ N ≥ R, F H R ⇒ F ≤ R
So, B > N ≥ R ≥ F
Conclusions
I. B © R ⇒ B > R      ( true)
II. F H N ⇒ F ≤ N       (true)
III. R \$ B ⇒ R < B       (true)
So, all I, II and III are true from the given statements.

1. Statements
D \$ M, M ∗ B, B δ J
Conclusions
II. B @ D
III. J @ M
1. I and II are true
2. I and III are true
3. II and III are true
4. I, II and III are true
5. None of the above

1. Statements
D \$ M ⇒ D < M,
M H B ⇒ M ≤ B, B δ J ⇒ B = J
So, D < M ≤ B = J
Conclusions
I. J © D ⇒ J > D       (true)
II. B @ D ⇒ B ≥ D       (false)
III. J @ M ⇒ J ≥ M       (true)

##### Correct Option: B

Statements
D \$ M ⇒ D < M,
M H B ⇒ M ≤ B, B δ J ⇒ B = J
So, D < M ≤ B = J
Conclusions
I. J © D ⇒ J > D       (true)
II. B @ D ⇒ B ≥ D       (false)
III. J @ M ⇒ J ≥ M       (true)
So, Conclusion I and III are true from the given statements.

1. Statements
W δ K, K © F, F \$ M
Conclusions
II. W @ F
III. F @ W
1. Only I is true
2. Only II is true
3. Only III is true
4. II and III are true
5. None of the above

1. Statements
W δ K ⇒ W = K,
K © F ⇒ K > F, F \$ M ⇒ F < M
So, W = K > F < M
Conclusions
I. M © K ⇒ M > K       (false)
II. W @ F ⇒ W ≥ F       (false)
III. F @ W ⇒ F ≥ w       (false)

##### Correct Option: E

Statements
W δ K ⇒ W = K,
K © F ⇒ K > F, F \$ M ⇒ F < M
So, W = K > F < M
Conclusions
I. M © K ⇒ M > K       (false)
II. W @ F ⇒ W ≥ F       (false)
III. F @ W ⇒ F ≥ w       (false)
So, no conclusion is true from the given statements.

1. Statements
L > M,
M > N,
N > P.
Conclusions
I. L > P
II. M > P
1. if only Conclusion I follows
2. if only Conclusion II follows
3. if either Conclusion I or II follows
4. if neither Conclusion I nor II follows
5. if both Conclusions I and II follow

1. Given that,
L > M ....(I)
M > N .....(II)
N > P .....(II)
On combining all the three statements, we get
L > M > N > P
Conclusions
I. L > P     (true)
II. M > P    (true)

##### Correct Option: E

Given that,
L > M ....(I)
M > N .....(II)
N > P .....(II)
On combining all the three statements, we get
L > M > N > P
Conclusions
I. L > P     (true)
II. M > P    (true)

So, it is clear that both Conclusions I and II follow from the given statements.

1. Statements
A > B,
B =H,
H > G
Conclusions
I. A > G
II. A > H
1. if only Conclusion I follows
2. if only Conclusion II follows
3. if either Conclusion I or II follows
4. if neither Conclusion I nor II follows
5. if both Conclusions I and II follow

1. Given that,
A > B     .....(I)
B = H     .....(ii)
H > G     ...(iii)
On combining the statement (i), (ii) and (iii), we get
A > B = H > G
Conclusions
I. A > G     (true)
II. A > H     (true)

##### Correct Option: E

Given that,
A > B     .....(I)
B = H     .....(ii)
H > G     ...(iii)
On combining the statement (i), (ii) and (iii), we get
A > B = H > G
Conclusions
I. A > G     (true)
II. A > H     (true)
So, it is clear that both Conclusions I and II follow from the given statements.