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Directions: In these questions, relationship between different elements is shown in the statement. The statements are followed by two conclusions. Choose the correct answer given below:
1
Statements: Y ≥ P = O,         P < R ≤ J
 
Conclusions: R > Y,       J > O
» Explain it
B
Statements: Y ≥ P = O,         P < R ≤ J

Conclusions: R > Y,       J > O

For conclusion I: R > I

Combining statements I and II, we get:

Y ≥ P < R

Here, we get opposite signs between Y and R and the given conclusion is R > Y, thus we cannot define any relation between R and Y. Hence, conclusion I does not follow.

For conclusion II: J > O

Combining statements I and II, we get:

O = P < R ≤ J

Here, the common sign between O and J is < and the given conclusion is J > O.
Therefore, conclusion II follows.

Hence option B is correct.
2
Statements:  T > D ≥ P ,      F ≥ P = R
 
Conclusions: T > R ,   D > F
» Explain it
A
Statements:  T > D ≥ P ,      F ≥ P = R
 
Conclusions: T > R ,   D > F

For conclusion I: T > R

Combining statements I and II, we get:

T > D ≥ P = R

Here, we can see the common sign between P and R is ‘>’.
Hence, conclusion I follows.

For conclusion II: D > F

Combining statements I and II, we get:

D ≥ P ≤ F

Here, we can see the opposite sign between D and F, thus no relationship can be established between them.
Therefore, conclusion II does not follow.

Hence option A is correct.
3
Statements:  C < D , E ≥ B , B > D , A = E
 
Conclusions:  B > C  ,  A < D
» Explain it
B
Checking C1:
 
B > D > C
 
Thus C1 follows.
 
Checking C2:
 
A = E ≥ B > D
 
Thus C2 does not follow.
 
Hence option B is correct.
4
Statement: M = X < Z ≥ W = N ≤ Q < T ≤ V = U

Conclusions: I. V ≥ W        II. T ≯  U
» Explain it
A
Statement: M = X < Z ≥ W = N ≤ Q < T ≤ V = U

Conclusions: I. V ≥ W        II. T ≯  U

Checking C1:
Here, if we move from V to W, we can observe the common sign of inequalities is '>' whereas the given conclusion I is V ≥ W. Hence, conclusion I doesn't follow.

Checking C2:
Here, moving from T to U, the common sign of inequalities is of '≤' which confirms that T is either less than or equal to U and the same can be interpreted as T is not greater than U. Conclusion II, which is T ≯  U, hence follows.

Option A is hence the correct answer.
 
5
Statement: P ≤ Q < S = T ≥ U ≥ W < Z
 
Conclusion:  I. S > W,        II. W = T
» Explain it
D
Statement: P ≤ Q < S = T ≥ U ≥ W < Z
 
Conclusion: S > W,        W = T

For conclusion I and II: S > W and W = T

From the given statement, we get:

S = T ≥ U ≥ W

Here, the common sign between S and W is ‘≥’ and the given conclusions are S > W and W = S.

Moreover, we are aware that 'S = T' which means we can replace T with S in conclusion 2.

Hence, either conclusion I or conclusion II follows.

Option D is hence the correct answer.