Question Details

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

Options

A

If only conclusion I is logically valid.

B

If only conclusion II is logically valid.

C

If neither conclusion I nor conclusion II is logically valid.

D

If both conclusion I and conclusion II are logically valid.

E

If either conclusion I or conclusion II is logically valid.

Show Answer

Correct Answer :

Option C

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. W<E=R<T
2. Q>W=S
3. ASC

Combining the statements to relate A, E, and R:
From statement (3), we have: AS
From statement (2), we have: S=W
So, combining these gives: AW
From statement (1), we have: W<E=R

Combining the relation between A, W, E, and R:

AW<E=R

From this chain, since AW and W<E, we strictly get:

A<E (or E>A)

And since E=R, we also get:

A<R (or R>A)

Evaluating Conclusion I: EA
Our derived relationship is strictly E>A. Therefore, EA (which includes the possibility of equality E=A) is not logically valid as equality is impossible.

Evaluating Conclusion II: R<A
Our derived relationship is strictly R>A. Therefore, Conclusion II (R<A) 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.

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