Question

which answers are examples of deductive reasoning? select each correct answer. the local grocery store charges $3 for a gallon of milk. joe is going to the local grocery store to buy milk. therefore, joe expects to spend $3 for a gallon of milk. mary and sue are friends. mary enjoys fishing, running, and rock climbing. sue likes fishing and rock climbing. sue must also like running. jonathan leaves for school at 7:30 a.m. and is on time. jonathan will always be on time if he leaves at 7:30 a.m. all three angles in an equilateral triangle measure 60°. triangle abc is an equilateral triangle. therefore, all three angles in triangle abc measure 60°

Explanation:

• Deductive reasoning starts from general premises and arrives at specific conclusions.
• For the first option: The general premise is the local grocery store's price for milk (\(\$3\) per gallon). The specific conclusion is Joe's expected spending.
• For the fourth option: The general premise is the angle measure in an equilateral triangle (\(60^{\circ}\)). The specific conclusion is about triangle \(ABC\).
• The second option is an incorrect assumption as just because Mary and Sue share some interests (fishing, rock - climbing), it doesn't mean Sue must like running (no general - to - specific logical flow based on established facts).
• The third option is an over - generalization. Just because Jonathan was on time once when leaving at \(7:30\) a.m., it doesn't mean he will always be on time (no solid general - to - specific logical connection based on a universal rule).

Answer:

The local grocery store charges \(\$3\) for a gallon of milk. Joe is going to the local grocery store to buy milk. Therefore, Joe expects to spend \(\$3\) for a gallon of milk.
All three angles in an equilateral triangle measure \(60^{\circ}\). Triangle \(ABC\) is an equilateral triangle. Therefore, all three angles in triangle \(ABC\) measure \(60^{\circ}\).