Statement : $W \le X, X \ge Y, Y < Z$
Conclusions: (I) $Z > X$
(II) $W > Y$
(III) $Y > W$
None of the conclusions (I), (II) and (III) are true.
To evaluate the truth of the given conclusions based on the statement, let's analyze each part:
Statement: W \le X, X \ge Y, Y < Z
Analysis:
- The first part of the statement W \le X implies that W is either less than or equal to X.
- The second part X \ge Y means X is greater than or equal to Y.
- The last part Y < Z indicates that Y is less than Z.
Conclusions:
- Z > X: The statement provides no direct comparison between Z and X. Y \lt Z and X \ge Y do not infer Z \gt X, as Z can be greater than or less than X. Therefore, Conclusion I is not definitely true.
- W > Y: From the statement, we have W \le X and X \ge Y, so W can indeed be lesser, equal, or greater than Y, but it is not definitively greater. Conclusion II is not definitely true.
- Y > W: According to the given statement, X \ge Y and W \le X; there is no definitive indication that Y is greater than W. So, Conclusion III is not definitely true.
Conclusion: None of the conclusions (I), (II), and (III) are definitely true.
Important Questions from Mathematical Inequalities
Directions: In the following question assuming the given statements to be true, find which of the conclusion(s) among given conclusions is/are definitely true and then give your answers accordingly.
Statement:
Y ≥ C < O ≥ F < R = B
Conclusions:
I. B > F
II. R > C
Directions: In each of the following questions assuming the given statement to be true, find which of the conclusions among given conclusions is / are definitely true and then give your answers accordingly.
Statement: E < U > L > K ≤ T = H ≤ Q
Conclusions:
I. U > H
II. T ≤ Q
Directions: In the following question assuming the given statements to be True, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.
Statements: Y > U ≥ Z ≥ K = X ≤ B ≤ A
Conclusions:
I. U = X
II. U > X
Directions: In each of the following questions assuming the given statement to be true, find which of the conclusions among given conclusions is/are definitely true and then give your answers accordingly.
Statement: S > L < P = T ≥ V > R
Conclusions:
I. P > R
II. S > V
In the question given, relations between different elements are shown in the statements. These statements are followed by two conclusions. Find out which of the given conclusions follow(s) the given statements and select the correct alternative from the given choices.
Statement:
L ≥ M = N < O, P < Q ≥ R = S ≥ L
Conclusion:
I. Q > M
II. N = Q
