1. Inductive reasoning
Inductive reasoning is a type of logic in which we observe specific phenomena and use those observations to make predictions about future similar phenomena. Inductive logic makes broad generalizations from specific observations. A perfect example is the hypothesis of the black crowds: All observed crows are black. Therefore, all crows are black. Here the observer is broadly generalizing the color of all the crows in the universe from the observation of a particular group of crows. Inductive reasoning goes from the specific to the general.
Now let’s analyze your examples.
A. Peaches cost $0.95/lb at the local store. Sue is going to buy 10 lb of peaches at the local store. Sue expects to pay $9.50 for peaches. This an example of deductive reasoning. We are going form the prices of the peaches at the local store to the price of Sue’s peaches. We are going from the general to the specific.
B. Last year, it rained every day in April. Next month is April. It will rain every day next month. Another example of inductive reasoning. The observer is inferring that Next April is going to rain based on the past observation of last year’s April.
C. John orders pizza for lunch every Friday. It is Friday. John will order pizza today. Again, inductive reasoning, and very similar to the previous one. The observer is broadly generalizing that John will order pizza today just because he ordered pizza on the same day in the past.
D. All cats are mammals. All mammals have kidneys. All cats have kidneys. In this example, the observer is not making predictions from past observations; rather they is using hypothesis to reach a logical conclusion. This is an example of deductive reasoning.
We can conclude that the B and C are examples of inductive reasoning.
2. Deductive reasoning
Deductive reasoning part from a general hypothesis (premise) to reach a specific logical conclusion. Deductive reasoning usually begins with premise, then a second premise, and based on those premises we reach a logical conclusion. For example, all men are mortal. Socrates is a man; therefore, Socrates is mortal. Here we have two premises and a logical conclusion. Deductive reasoning goes from the general to the specific.
A. 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. Here, the observer is making a broad generalization from a specific observation; therefore, this is an example of inductive reasoning.
B. All three angles in an equilateral triangle measure 60°. Triangle ABC is an equilateral triangle. Therefore, all three angles in triangle ABC measure 60°. This is an example of deductive reasoning. Here we are using general hypotheses (All three angles in an equilateral triangle measure 60°. Triangle ABC is an equilateral triangle) to reach a logical conclusion (all three angles in triangle ABC measure 60°).
C. Mary and Sue are friends. Mary enjoys fishing, running, and rock climbing. Sue likes fishing and rock climbing. Sue must also like running. This is another example of deducting reasoning. Even though the conclusion may or may not be true, we are using premises (hypothesis) to reach that conclusion rather than past observations.
D. 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. This is an example of deductive reasoning. Here we are going from the general price of the milk at the local store to the specific price of the milk Joe is going to buy.
We can conclude that B, C, and D are examples of deductive reasoning.
