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).
 Statements
H ≥ I = J > K ≤ L
Conclusions
I. K < H
II. L ≥ I

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Given that,
H ≥ I = J > K ≤ L
Here, statements are already combined
H ? I = J > K means H > K
Conclusions
I. K < H (true)
II. L ≥ I (false)Correct Option: A
Given that,
H ≥ I = J > K ≤ L
Here, statements are already combined
H ? I = J > K means H > K
Conclusions
I. K < H (true)
II. L ≥ I (false)
So, it is clear that only Conclusion I follows from the given statements.
 Statements
S > C ≥ 0, P < C
Conclusions
I. 0 < P
II. S > P

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Given that
S > C ≥ O ....(i)
P < C ...............(ii)
On combined the statement (i) and (ii), we get
S > C > P
P < C ≥ O
Conclusions
I. O < P............... (false)
II. S > P ................ (true)Correct Option: A
Given that
S > C ≥ O ....(i)
P < C ...............(ii)
On combined the statement (i) and (ii), we get
S > C > P
P < C ≥ O
Conclusions
I. O < P............... (false)
II. S > P ................ (true)
So, it is clear that only Conclusion II follow from the given statements.
 Statements
A = B ≤ C,
A > R
Conclusions
I. B > R
II. R < C

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Given that,
A = B ≤ C ................(i)
A > R .........................(II)
On combining the statements (i) and (ii), we get
R < A = B ≤ C
Conclusion
I. B > R. .................(true)
II. R < C .................(true)Correct Option: E
Given that,
A = B ≤ C ................(i)
A > R .........................(II)
On combining the statements (i) and (ii), we get
R < A = B ≤ C
Conclusion
I. B > R. .................(true)
II. R < C .................(true)
So, it is clear that both Conclusions I and II follow from the given statements.
 Statements
D > E ≤ F,
J < F
Conclusions
I. D > J
II. E < J

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Given that,
D > E ≤ F ..............(i)
J < F .........................(ii)
On combining the statements (i) and (ii), we get
D > E ≤ F > j
Conclusions
I. D > J
II. E < JCorrect Option: D
Given that,
D > E ≤ F ..............(i)
J < F .........................(ii)
On combining the statements (i) and (ii), we get
D > E ≤ F > j
Conclusions
I. D > J (false)
II. E < J (false)
So, it is clear that neither Conclusion I nor II is true .