Consider the following two statements: 1. *All supersonic aircraft are equipped with afterburning engines.* 2. *Some military UAVs are supersonic aircraft.* Which of the following conclusions logically and necessarily follows from the given statements?

(A) Some military UAVs are equipped with afterburning engines.

(B) All military UAVs are equipped with afterburning engines.

(C) All aircraft with afterburning engines are military UAVs.

(D) No military UAV is equipped with an afterburning engine.

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Set Theory Representation:** Let $S$ = supersonic aircraft, $E$ = afterburning engines, $U$ = military UAVs. 2. **Stage 2: Premises:** * Statement 1: $S \subseteq E$. * Statement 2: $U \cap S \ne \emptyset$. 3. **Stage 3: Deduction:** Since $U \cap S$ is non-empty, and every element of $S$ is in $E$, it follows that $(U \cap S) \subseteq (U \cap E) \ne \emptyset$. 4. **Stage 4: Translation:** Therefore, 'Some military UAVs are equipped with afterburning engines.' 5. **Stage 5: Distractor Analysis:** Option B generalizes 'some' to 'all' (unwarranted). Option C reverses inclusion. Option D contradicts Statement 1 & 2.

← Prev Question Next Question →