Given the statements: 1. No drone is a manned spacecraft. 2. All hypersonic gliders are drones. Which of the following conclusions logically follows beyond doubt?

(A) No hypersonic glider is a manned spacecraft

(B) Some hypersonic gliders are manned spacecraft

(C) All drones are hypersonic gliders

(D) No manned spacecraft is an aircraft

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles Using categorical logic: - Let $D$ = Drones - Let $M$ = Manned spacecraft - Let $H$ = Hypersonic gliders Premise 1: $D \cap M = \emptyset$ (No $D$ is $M$) Premise 2: $H \subseteq D$ (All $H$ are $D$) ### 2. Analytical Deduction Since every element of $H$ is in $D$, and no element of $D$ is in $M$, it follows unconditionally that no element of $H$ can be in $M$: $$H \cap M = \emptyset \implies \text{No hypersonic glider is a manned spacecraft}$$ (This is the classical valid syllogism *Celarent*: EAE-1). ### 3. Distractor Forensics - **Option A:** Correct necessary conclusion. - **Option B:** Directly contradicts the valid conclusion. - **Option C:** Illicit conversion of universal affirmative statement ($H \subseteq D \not\implies D \subseteq H$). ### 4. Exam Trap & Standard Reference - **Trap Alert:** EAE-1 categorical deduction is universally valid. - **Standard Reference:** Copi, I.M., *Introduction to Logic*.

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