1. Create a truth table for ~p ∧ q
2. Create a truth table for p ∨ ~q
3. Create a truth table for (p ∧ q) → r
4. Create a truth table for ~p → q
5. Create a truth table for (p ∨ q) ↔ r
6. Create a truth table for p ↔ ~q

Write the converse, inverse, and contrapositive of each statement.

1. If it is raining, then the game is cancelled.
2. If you study, then you will be prepared for the test.
3. If Stacy doesn’t like to cook, then she marries a chef.
4. If Jose wants to go to the party, then he must clean his room.
5. If Jamal doesn’t practice, then he won’t do well in the game.
6. If Sarah doesn’t like cookies, then she won’t be friends with Cookie Monster.

Write a statement that is equivalent to the given statement.

1. If it is cold out, then you should wear a coat.
2. If the sun isn’t shining, then I don’t need my sunglasses.
3. If Haley is lactose intolerant, then she doesn’t drink milk.
4. If Harold is gluten intolerant, then he can’t eat a sandwich.
5. If Ron doesn’t like crowds, then he stays home during festivals.
6. If Jackie likes to read, then she doesn’t watch much TV.

Determine if the following examples are inductive or deductive reasoning.

1. A recruiter notices that the last five employees she hired all graduated from Northwest Florida State College and are doing well in their positions. She makes a conjecture that all Northwest Florida State College grads will do well at her company.
2. I pull a coin from my wallet, and it is a penny. I pull a second coin from my wallet, and it is also a penny. Therefore, all the coins in my wallet must be pennies.
3. All the coins in my wallet are pennies. Therefore, I will pull out a penny if I randomly pick a coin.

Negate each statement below.

1. All teachers are poor.
2. No cheaters pass.
3. Some people are not born lucky.
4. Some dogs are mean.
5. If it’s hot, then Sam goes to the beach.
6. If I write a test, then it’s not hard.
7. If you don’t like cookies, then you are not Cookie Monster.
8. I like cookies and I like milk.
9. The sky is blue or the grass is purple.
10. I have to stay home and you can’t go either.
11. The tuition is low or there are lots of scholarships available.

Draw a valid conclusion from each set of premises.

1. If you have a cat, then you have a pet. Jane has a cat.
2. If more is spent on research, medical science will advance.  More is not spent on research.
3. If you go to the beach, then you wear sunscreen.  If you wear sunscreen, then you won’t get burnt.
4. John likes cookies or milk. John doesn’t like milk.