# Conditional claims are surprisingly tricky. Imagine that a coworker tells you, “If it’s raining, then I will bring an umbrella.” Now imagine you see that they brought an umbrella. Can you conclude that it’s raining? Why or why not?

Think back to the conversations you’ve had during the last week. Give an example of a deductive argument and an inductive argument that you or your interlocutor made. For each of these arguments, list the premises and the conclusion. Was the deductive argument valid? Was the inductive argument strong? Why or why not, exactly?

2. Determine the antecedent, consequent, necessary condition, and sufficient condition for the following claims:

a. If TyQuana scores a 95% on her final, then she will pass the course.

b. Foods are nutritious if they positively contribute to the overall diet of a person.

c. Water-saving measures are effective means for communities to deal with severe drought only if enough people participate in those measures.

3. We all want to be consistent in our thoughts — that is, we don’t want to contradict ourselves. That being said, we often don’t live up to this intellectual ideal. Give an example of a time you contradicted yourself. How did you resolve the contradiction? Specifically, which of the inconsistent beliefs did you give up?

4. Conditional claims are surprisingly tricky. Imagine that a coworker tells you, “If it’s raining, then I will bring an umbrella.” Now imagine you see that they brought an umbrella. Can you conclude that it’s raining? Why or why not?

5. Construct a counterexample to demonstrate that the following arguments are invalid. First, remove the material content and use variables to show the argument form, and second, substitute new material content into the form to show the counterexample.

For example:
All dogs are canines
No cats are dogs
No cats are canines

Has the form:
All M are P
No S are M
No S are P

Counterexample through substitution:
All dogs are mammals
No cats are dogs
No cats are mammals

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a. If Tom is dead, then he was executed.
Tom was executed.