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
Analyzing Inequality Statement
The given statement is:
$F < B < E ≤ C = D ≥ A < G$
Let's break down the relationships:
- From the statement, we can establish the following direct and indirect relationships:
- $F$ is less than $B$.
- $B$ is less than $E$.
- $E$ is less than or equal to $C$.
- $C$ is equal to $D$.
- $D$ is greater than or equal to $A$.
- $A$ is less than $G$.
- Combining these, we get a chain: $F < B < E ≤ C = D ≥ A < G$.
Evaluating Conclusion I
Conclusion I: $G < F$
From the combined chain $F < B < E ≤ C = D ≥ A < G$, we can clearly see that $F$ is less than $G$ ($F < G$). Therefore, the conclusion $G < F$ is definitely FALSE.
Evaluating Conclusion II
Conclusion II: $C > G$
We know that $C = D ≥ A < G$. This means $C$ is related to $G$ through $D$ and $A$.
- $C$ is equal to $D$.
- $D$ is greater than or equal to $A$.
- $A$ is strictly less than $G$.
Consider these scenarios:
- If $C = D = 10$, $A = 5$, and $G = 11$, then $C < G$.
- If $C = D = 10$, $A = 9$, and $G = 10$, then $C = G$.
- If $C = D = 10$, $A = 5$, and $G = 9$, then $C > G$.
Since there are possible scenarios where $C > G$ is not true ($C < G$ or $C = G$), Conclusion II is NOT definitely TRUE.
Final Determination
Conclusion I is FALSE. Conclusion II is not definitely TRUE.
Therefore, neither Conclusion I nor Conclusion II is definitely 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
