Mathematical operation and symbol notation
 In which of the following expressions does the expression 'M' > R' does not hold true ?

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We can check all the options one by one.
from option (a),
M = P > Q > R ⇒ M > R
So, expression M > R holds true for option (a).
From option (b),
M > P ≥ Q = R ⇒ M > R
So, expression M > R holds true for option (b).
From option (c).
R = P < Q < M ⇒ R < M
So, expression M > R holds true for option (c).
From option (d),
R < Q ≤ P = M ⇒ R < M
So, expression M > R holds true for option (d)
From option (e),
M = P < Q = R ⇒ M < RCorrect Option: E
We can check all the options one by one.
from option (a),
M = P > Q > R ⇒ M > R
So, expression M > R holds true for option (a).
From option (b),
M > P ≥ Q = R ⇒ M > R
So, expression M > R holds true for option (b).
From option (c).
R = P < Q < M ⇒ R < M
So, expression M > R holds true for option (c).
From option (d),
R < Q ≤ P = M ⇒ R < M
So, expression M > R holds true for option (d)
From option (e),
M = P < Q = R ⇒ M < R
So, expression M > R does not hold true for option (e).
 In which of the following expression will the expression ' A < D' be definitely true ?

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Try all option one by one.
Correct Option: C
Try all option one by one.
From the expression "C "
A < B = C ≤ D,
A < D will be definitely true .
 Which of the following expression will be true, if the given expression K ≥ G > H ≤ F is definitely true ?

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Now, we can check all the options one by one
(a) F ≥ K
Given equation,
1. K ? G > H ? F
Then relation between F and K will be from 1,
2. K ? H ? F (cannot decide between K and F)
(b) H < K
from 1. Relation between H and K will be
3. K ? G > H
from 3
H < K
(c) F < G
Relation between F and G from 1,
G > H ? F (cannot decide between G and F)
(d) K ≥ H
Relation Between K and H,
From 1. K ? G > H means K > HCorrect Option: B
Now, we can check all the options one by one
(a) F ≥ K......(false)
(b) H < K .......(true)
(c) F < G ......(false)
(d) K ≥ H ......(false)
So, it clear that option (b) true ,
 Statements
P > M > Q,
Q > Z > N
Conclusions
I. M ≥ Z
II. N < P

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Given that,
i. P > M > Q
ii. Q > Z > N
On combining the statement (i) and (ii) we get
P > M > Q > Z > N
Conclusions
I. M ≥ Z (false)
II. N < P (true)Correct Option: B
Given that,
i. P > M > Q
ii. Q > Z > N
On combining the statement (i) and (ii) we get
P > M > Q > Z > N
Conclusions
I. M ≥ Z (false)
II. N < P (true)
So, it is clear that only Conclusion II follows from the given statements.
 Statements
A < B < C ≤ D = E
Conclusions
I. B ≤ E
II. B < E

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Given that,
A < B < C ≤ D = E
Here, statements are already combined.
Conclusions
I. B ≤ E (false)
II. B < E (true)Correct Option: E
Given that,
A < B < C ≤ D = E
Here, statements are already combined.
Conclusions
I. B ≤ E (false)
II. B < E (true)
So, it is clear that only Conclusion II follow from the given statements.