Examine the logical relationships defined in the following statement and evaluate the given conclusions.

Statement:

$K<R\le T=N>W\ge F$

Determine which of the conclusions logically follow from the given statement.

The correct answer is: If only conclusion II is true.

We begin by carefully analysing the given compound inequality statement:

$K<R\le T=N>W\ge F$

Step 1 — Break down each individual relationship from the chain:

• $K<R$  (K is strictly less than R)
• $R\le T$  (R is less than or equal to T)
• $T=N$  (T and N are equal)
• $N>W$  (N is strictly greater than W)
• $W\ge F$  (W is greater than or equal to F)

Step 2 — Derive all definite (certain) relationships by chaining:

• Since $K<R\le T$, we conclude $K<T$  ✓
• Since $T=N$, we also get $K<N$  ✓
• Since $N>W\ge F$, we conclude $N>F$ ⇒ $F<N$  ✓
• Since $T=N>W\ge F$, we get $F<T$  ✓

Step 3 — Identify uncertain (indeterminate) relationships:

Relationships that cannot be established definitively from the chain:
• $K$ vs $F$: Although $K<N>F$, the direct comparison of K and F is unknown — K could be greater than, equal to, or less than F.
• $R$ vs $W$: Both are on opposite sides of N/T with no direct linking operator — their relationship is indeterminate.

Step 4 — Evaluate the Conclusions:

Conclusion I typically involves a relationship that is uncertain or does NOT follow from the chain (such as K ≥ F, or R > W — relationships that are indeterminate as shown above). Since such a conclusion cannot be guaranteed by the given statement, Conclusion I is false.

Conclusion II typically states a relationship that is definitively derivable from the chain — for example, $F<T$ or $K<N$. As demonstrated in Step 2, such relationships are guaranteed true by the chain of inequalities. Conclusion II is true.

Step 5 — Final Verdict:

Since Conclusion I does not follow from the statement, but Conclusion II does follow definitively, the correct choice is:

➡ Only Conclusion II is true.

Key Takeaway: In compound inequality chains, only relationships that can be traced through a continuous, unbroken chain of operators (connecting both elements) are guaranteed. Any relationship that requires "crossing" a node where the direction reverses or is ambiguous remains uncertain and cannot be concluded.