Statement:
$P \ge T ; Q = R \ge U ; V \ge R > S ; T \ge Q$
Conclusions:
I: $V \ge Q$
II: $P > S$
Analyze Logical Reasoning Statement and Conclusions
The question requires identifying the FALSE conclusion based on a given statement containing inequalities.
Statement Breakdown
The given statement can be broken down into the following relationships:
- $P \ge T$
- $Q = R \ge U$
- $V \ge R > S$
- $T \ge Q$
Evaluating Conclusion I: $V \ge Q$
We need to determine if the relationship $V \ge Q$ is true.
- From the statement, we have the equality $Q = R$.
- We also know that $V \ge R$.
- By substituting $R$ with $Q$ (since $Q=R$), the inequality $V \ge R$ becomes $V \ge Q$.
- Therefore, Conclusion I is TRUE.
Evaluating Conclusion II: $P > S$
We need to determine if the relationship $P > S$ is true.
Let's combine the relevant inequalities from the statement to form a chain:
$P \ge T$
$T \ge Q$
$Q = R$
$R > S$
Combining these gives the sequence: $P \ge T \ge Q = R > S$.
Since $R > S$, and $P \ge T \ge Q = R$, it logically follows that $P$ must be greater than $S$.
Therefore, Conclusion II is TRUE.
Identifying the False Conclusion
Our analysis shows that both Conclusion I ($V \ge Q$) and Conclusion II ($P > S$) are TRUE based on the provided statement.
The question asks to identify the conclusion that is FALSE.
Since neither Conclusion I nor Conclusion II is false, the correct answer is that Neither I nor II is false.
Similar Questions
In this question, some equations are solved on the basis of a certain system. On the same basis, find out the correct answer from amongst the four alternatives for the unsolved equation:
462 = 551
398 = 487
856 = ?Find the missing number in the series:
8 6 7 9 13 11 3 7 ? In this question, some equations are solved on the basis of a certain system. On the same basis find out the correct answer from amongst the four alternatives for the unsolved equation.
7x6x8=678
8x9x7=987
6x5x7=567
5x4x6=?Select the missing number from the given alternatives:
7 9 8 8 9 ? 4 9 6 60 90 70 Select the missing number from the given matrix:
Select the missing numbers from the given alternatives:
? 120 150 110 100 90 80 60 40 If 37*14 = 17, 69*33 = 34, 91*125 = 72, then what should 28*56 = ?
Select the missing numbers from the given responses.
If 3 *4 = 10, 5 *8 = 18, 7 *7 =?
In the following question, a series is given with one term missing. Choose the correct alternative from the given ones that will complete the series.
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
