Given the statements: - $P = Q \geq R$ - $Q \geq S T$ - $U U$ III. $P = T$ IV. $R P$

Question

Given the statements:

- $P = Q \geq R$
- $Q \geq S > T$
- $U < R$

Determine which of the following conclusions are true:

I. $P \geq S$

II. $Q > U$

III. $P = T$

IV. $R > P$

Accepted Answer

**Solution:** 1. Given statements: - $P = Q \geq R$ - $Q \geq S > T$ - $U < R$ 2. From $P = Q \geq R$ and $Q \geq S > T$, we can combine as: - $P = Q \geq R$ - $Q \geq S > T$ 3. Check each conclusion: - **I. $P \geq S$** - Since $P = Q$ and $Q \geq S$, it follows that $P \geq S$. - Therefore, conclusion I is **true**. - **II. $Q > U$** - Given $U < R$ and $Q \geq R$, so $Q > U$. - Therefore, conclusion II is **true**. - **III. $P = T$** - Since $P = Q \geq S > T$, $P$ is greater than $T$, not equal. - Therefore, conclusion III is **false**. - **IV. $R > P$** - Given $P = Q \geq R$, so $P$ is greater than or equal to $R$, not less. - Therefore, conclusion IV is **false**. **Answer:** Both I and II are true.

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