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. $M = R$
Logical Reasoning: Inequality Statements Analysis
Analyzing the Statements
The problem provides several inequality statements relating different variables:- $J > K = L$
- $M \geq N < K$
- $O < J < P$
- $N = Q \geq R$
Evaluating the Conclusions
We need to determine the truthfulness of the following conclusions based on the statements:- I. $M > R$
- II. $M = R$
Deducing the Relationship between M and R
To evaluate the conclusions, let's combine the relevant statements. We are interested in the relationship between $M$ and $R$.- From statement 2: $M \geq N$
- From statement 4: $N = Q \geq R$
Assessing Conclusion Truthfulness
The derived relationship $M \geq R$ means that either $M$ is strictly greater than $R$ ($M > R$) or $M$ is equal to $R$ ($M = R$).- Can Conclusion I ($M > R$) be true? Yes. Consider a scenario where $M$ is greater than $N$, and $N=Q$, and $Q$ is greater than $R$. For example, let $M=5$, $N=4$, $Q=4$, $R=3$. This satisfies $M \geq N = Q \geq R$. In this case, $M > R$.
- Can Conclusion II ($M = R$) be true? Yes. Consider a scenario where $M=N$, $N=Q$, and $Q=R$. For example, let $M=4$, $N=4$, $Q=4$, $R=4$. This satisfies $M \geq N = Q \geq R$. In this case, $M = R$.
Determining the Correct Option
The logical deduction aligns with the option stating that one of the two conclusions must be true. Therefore, the correct choice is "Either conclusion I or II is true".Similar Questions
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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
