Given the following premises:
1. Every harvester deployed on the farm is equipped with GPS tracking.
2. Some harvesters deployed on the farm are autonomous.
3. No autonomous vehicle operates without a failsafe emergency stop.
Which of the following conclusions CAN be logically deduced?
Options:
(A) Some machines equipped with GPS tracking have failsafe emergency stops.
(B) All machines equipped with GPS tracking are autonomous.
(C) Some harvesters deployed on the farm have failsafe emergency stops.
(D) No machine with a failsafe emergency stop is equipped with GPS tracking.
Answer Key:
A, C
Step-by-Step Solution & Explanation
**Method 1: Predicate Logic & Venn Set Overlaps**
Let $H$ be harvesters on the farm, $G$ be machines with GPS, $A$ be autonomous machines, and $F$ be machines with failsafe stops.
- Premise 1: $H \subseteq G$.
- Premise 2: $H \cap A \neq \emptyset$. Let $x \in H \cap A$.
- Premise 3: $A \subseteq F$.
From $x \in H \cap A$, since $H \subseteq G$ and $A \subseteq F$, we have $x \in G$ and $x \in F$. Thus $G \cap F \neq \emptyset$.
- Conclusion A: 'Some machines equipped with GPS tracking have failsafe emergency stops' ($G \cap F \neq \emptyset$) is TRUE.
- Conclusion B: 'All machines with GPS are autonomous' ($G \subseteq A$) is false/not guaranteed.
- Conclusion C: 'Some harvesters on the farm have failsafe emergency stops' ($H \cap F \neq \emptyset$, since $x \in H$ and $x \in F$) is TRUE.
- Conclusion D: Contradicts A.
Thus, the correct options are **A** and **C**.