**Statements:**

P ≤ Q

Question

**Statements:**

P ≤ Q < R = S ≥ T; U = R ≥ V ≤ W

**Conclusions:**

I. P < W
II. T ≤ U

Choose the correct option based on the conclusions that logically follow from the statements.

Accepted Answer

**Solution:**

1. Given statements:
   - P ≤ Q < R = S ≥ T
   - U = R ≥ V ≤ W

2. From the first statement, we have the order:
   $$P \leq Q < R = S \geq T$$
   This means:
   - P is less than or equal to Q
   - Q is less than R
   - R equals S
   - S is greater than or equal to T

3. From the second statement:
   $$U = R \geq V \leq W$$
   This implies:
   - U equals R
   - R is greater than or equal to V
   - V is less than or equal to W

4. Analyze Conclusion I: *P < W*
   - From the statements, we know P ≤ Q < R and V ≤ W.
   - However, there is no direct relation between P and W.
   - Since P ≤ Q < R and R ≥ V ≤ W, P could be less than or equal to W, but not necessarily less than W.
   - Therefore, conclusion I does not necessarily follow.

5. Analyze Conclusion II: *T ≤ U*
   - From the first statement, S ≥ T and R = S, so R ≥ T.
   - From the second statement, U = R.
   - Therefore, U = R ≥ T, which implies T ≤ U.
   - Hence, conclusion II logically follows.

**Answer:** (b) If only conclusion II is true

Answer

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