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
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: $V > T$
- A statement is given followed by two conclusions. Find which conclusion is FALSE based on the given statement.
Statement:
$P \ge T ; Q = R \ge U ; V \ge R > S ; T \ge Q$
Conclusions:
I: $V \ge Q$
II: $P > S$ 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
