1. Intro to Conditional Statements

$$p\rightarrow q$$  

$$q\rightarrow p$$  

$$\sim q\rightarrow\sim p$$  

$$\sim p\rightarrow\sim q$$  

You are an American citizen.

You have the right to vote.

You are not an American citizen.

You do not have the right to vote.

You are an American citizen.

You have the right to vote.

You are not an American citizen.

You do not have the right to vote.

$$\sim p\rightarrow q$$

$$\sim p\rightarrow\sim q$$

$$p\rightarrow q$$

$$p\rightarrow\sim q$$

I did not go to the store

I went to Shaws

I did not leave the house

I went home

If an object is made of gold, then it is a ring.

If an object is not a ring, then it is not made of god.

If an object is not made of gold, then it is not a ring.

There is no converse of the statement.

If an object can fly, then it is a bird.

If an object is not a bird, then it cannot fly

If an object cannot fly, then it is not a bird

There is no converse of the statement

If I don't study for the test, then I will not get a good grade.

If I did not get a good grade, then I did not study for the test.

If I get a good grade, then I studied for the test.

p→q

p↔q

~p→ ~q

q→p

If I don't study for the test, then I will not get a good grade.

If I get a good grade, then I studied for the test.

If I did not get a good grade, then I did not study for the test.

$$p\rightarrow q$$  

$$p\leftrightarrow q$$  

$$\sim p\rightarrow\ \sim q$$  

$$\sim q\rightarrow\sim p$$