Active Learning Exercises: Deductive Reasoning

Identify Necessary vs Sufficient Conditions

1. Being 18 years old is a ______ condition for being older than 16 years old.

2. Being at least 35 years old is a ______ condition for being President of the United States.

3. Being an opossum is a ______ condition for being a marsupial.

4. Being a mythical creature is a ______ condition for being a unicorn.

Identify the Type of Deductive Reasoning

1. If I wish to withdraw from a class, then I’ll complete a Registration Form. I will not complete the form. Therefore, I do not wish to withdraw.

2. Some cats are not gray. All gray things are colored. Ergo, some cats are not colored.

3. A circle is not the same type of shape as a square.

4. Bernie or Amir cook tonight. Bernie does not cook. Therefore, Amir cooks tonight.

5. All garlic is tasty. Some plants are not tasty. Therefore, not all plants are garlic.

6. If feet had wings, pigs could fly. If pigs could fly, I’d own a farm called “Where Pigs Fly.” Thus, if feet had wings, I’d own that farm.

7. If it snowed, the school is closed. It snowed. Therefore, the school is closed.

8. Triangle A is congruent to Triangle B. Triangle A is isosceles. Therefore, Triangle B is isosceles.

9. Adele trespassed. Therefore, she intentionally entered someone’s land without consent or necessity.

Counterexample Exercise

Identify the correct counterexample to this argument:

P1) If it snowed, the school is closed.
P2) The school is closed.
C) Therefore, it snowed.

Options:
a) It did not snow but school is closed for the holidays
b) It did not snow but the school is closed because of flooding
c) It did snow but the school is closed because of flooding
d) A and B
e) A, B, and C

Counterargument Exercise

Original argument form:

Some fruit are green.
Some fruit are apples.
Therefore, some fruit are green and apples.

Task: Create your own counterargument to show the invalidity of the form.