Statements: $$ \text{ All apples are fruits.} $$ $$ \text{ All fruits are tasty.} $$ Conclusions: $$ \text{I. All apples are tasty.} $$ $$ \text{ II. Some tasty things are apples.} $$
\[ \textbf{Statements:} \\ 1. \; \text{All apples are fruits.} \\ 2. \; \text{All fruits are tasty.} \] \[ \textbf{Conclusions:} \\ I. \; \text{All apples are tasty.} \\ II. \; \text{Some tasty things are apples.} \] \[ \textbf{Step 1: Analyze Conclusion I.} \] From the statements: \[ \text{All apples } \subseteq \text{fruits}, \quad \text{All fruits } \subseteq \text{tasty}. \] By transitivity: \[ \text{All apples } \subseteq \text{tasty}. \] Hence, Conclusion I follows. \[ \textbf{Step 2: Analyze Conclusion II.} \] Since all apples are tasty, it directly implies: \[ \text{Some tasty things are apples.} \] Hence, Conclusion II also follows. \[ \textbf{Final Answer: Both Conclusion I and II follow.} \]
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