For the following question, analyze the relationships between the elements as defined in the statements and determine which of the accompanying conclusions is logically valid.
Statements:
W < E = R < T, Q > W = S, A ≤ S ≤ C
Conclusions:
I: E ≥ A
II: R < A
Correct Answer :
If neither conclusion I nor conclusion II is logically valid.
Solution :
To determine which conclusion is logically valid, let us combine and analyze the given statements step-by-step.
Given Statements:
1.
2.
3.
Combining the statements to relate , , and :
From statement (3), we have:
From statement (2), we have:
So, combining these gives:
From statement (1), we have:
Combining the relation between , , , and :
From this chain, since and , we strictly get:(or )
And since , we also get:(or )
Evaluating Conclusion I:
Our derived relationship is strictly . Therefore, (which includes the possibility of equality ) is not logically valid as equality is impossible.
Evaluating Conclusion II:
Our derived relationship is strictly . Therefore, Conclusion II () is completely contradictory and false.
Thus, neither conclusion I nor conclusion II is logically valid.
The correct answer is: If neither conclusion I nor conclusion II is logically valid.
Access expert-curated educational resources and study materials—completely free.
Create, conduct, and manage professional online assessments with Mindyard. Perfect for teachers and institutes.
Copyright © 2026 Mindyard. All Rights Reserved.