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.
 Statements
B © N, N @ R, F ∗ R
Conclusions
I. B © R
II. F ∗ N
III. R $ B

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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.
 Statements
D $ M, M ∗ B, B δ J
Conclusions
I. J © D
II. B @ D
III. J @ M

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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.
 Statements
W δ K, K © F, F $ M
Conclusions
I. M © K
II. W @ F
III. F @ W

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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.
 Statements
L > M,
M > N,
N > P.
Conclusions
I. L > P
II. M > P

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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.
 Statements
A > B,
B =H,
H > G
Conclusions
I. A > G
II. A > H

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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.