Given the following two premises: 1. All supersonic aircraft are equipped with titanium skin panels. 2. Some experimental gliders are supersonic aircraft. Which of the following conclusions logically follows beyond doubt from the given premises?

(A) Some experimental gliders are equipped with titanium skin panels

(B) All experimental gliders are equipped with titanium skin panels

(C) No experimental gliders are equipped with titanium skin panels

(D) All aircraft equipped with titanium skin panels are supersonic aircraft

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles Using standard formal categorical syllogisms or Euler / Venn diagrams: - Let $S$ = Supersonic aircraft - Let $T$ = Aircraft equipped with titanium skin panels - Let $G$ = Experimental gliders Premise 1: All $S$ are $T$ ($S \subseteq T$) Premise 2: Some $G$ are $S$ ($G \cap S \neq \emptyset$) ### 2. Analytical Formulation Since $G \cap S$ is non-empty, there exists at least one element $x$ such that $x \in G$ and $x \in S$. Since every element of $S$ is in $T$ ($S \subseteq T$), it follows that $x \in T$. Therefore, $x \in G \cap T$, which establishes that: $$\text{Some } G \text{ are } T$$ ### 3. Step-by-Step Option Check - **Some experimental gliders are equipped with titanium skin panels:** Directly and indisputably valid (Darii syllogism: AII-1). - **All experimental gliders...:** Invalid; Premise 2 only specifies *some* gliders. - **No experimental gliders...:** Directly contradicts the valid conclusion. - **All aircraft with titanium skin panels are supersonic:** Affirming the consequent / illicit conversion of universal affirmative statement ($S \subseteq T \not\implies T \subseteq S$). ### 4. Exam Trap & Standard Reference - **Trap Alert:** Do not perform illicit conversion of universal affirmatives ("All A are B" does not mean "All B are A"). - **Standard Reference:** Copi, I.M., *Introduction to Logic*, 14th Edition, Routledge.

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