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
A statement is given followed by two conclusions. Find which conclusion is TRUE based on the given statement.
Statement:
C < A ≤ T = D ≥ O; G ≥ D < S; T ≥ A
Conclusions:
I: A ≤ O
II: C < G
The given statements are followed by two conclusions. Find out which conclusion is FALSE based on the given statements.
Statements:
J > K = L, M ≥ N < K, O < J < P, N > Q > R
Conclusions:
I. P > M
II. N < P
A statement is given followed by two conclusions. Find which conclusion is TRUE based on the given statement.
Statement:
$P \ge T; Q = R \ge U; V \ge R < S; T \ge Q$
Conclusions:
I: $T \ge U$
II: $V > T$
The given statements are followed by two conclusions. Find out which conclusion is TRUE based on the given statements.
Statements:
$J > K = L, M \geq N < K, O < J < P, N = Q \geq R$
Conclusions:
I. $M > R$
II. $M = R$Read the given statement and conclusions carefully. Decide which of the given conclusions is/are definitely TRUE from the statement.
Statement: F < B < E ≤ C = D ≥ A < G
Conclusion I: G < F
Conclusion II: C > G
Important Questions from Mathematical Inequalities
Which figure should replace the question mark (?) in the following series to continue the pattern?
Select the option that is related to the third term in the same way as the second term is related to the first term and the sixth term is related to the fifth term.
400 : 200 :: 248 : ? :: 256 : 128
Which of the following option figures will complete the pattern in the figure given below?
A square sheet of paper is folded along the dotted line successively along the directions shown and is then punched in the last. How would the paper look when unfolded?
Select the correct combination of mathematical signs that can sequentially replace the * signs and balance the given expression.
23 * 9 * 13 * 96 * 2 * 92
