Given the statements: $$D O \leq M = I A \geq T E$$ Determine which of the following conclusions follow: I. $M E$ II. $O A$ IV. $D = E$

Question

Given the statements: $$D > O \leq M = I < N; \quad I > A \geq T > E$$ Determine which of the following conclusions follow: I. $M > E$ II. $O < T$ III. $N > A$ IV. $D = E$

Accepted Answer

**Solution:** 1. Given statements: - $D > O \leq M = I < N$ - $I > A \geq T > E$ 2. From the first statement, we have: - $D > O$ - $O \leq M$ - $M = I$ - $I < N$ 3. From the second statement: - $I > A$ - $A \geq T$ - $T > E$ 4. Combining the inequalities: - Since $M = I$, and $I > A \geq T > E$, it follows that: $$M = I > A \geq T > E$$ - Also, $O \leq M = I \geq T$, so the relation between $O$ and $T$ is not definite. - From $I < N$ and $I > A$, we get: $$N > I > A$$ 5. Evaluate conclusions: - I. $M > E$: - Since $M = I > A \geq T > E$, $M > E$ is true. - II. $O < T$: - $O \leq M = I \geq T$, but no definite relation between $O$ and $T$; so this is false. - III. $N > A$: - $N > I > A$, so $N > A$ is true. - IV. $D = E$: - $D > O \leq M = I \geq T > E$, no equality between $D$ and $E$; so false. **Answer:** Both I and III follow.

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