Goals

1. Understand what a proposition is.
2. Understand what a truth value is.
3. Complete the short quiz below.

What is Logic?

Logic is the fundamental tool used for arguments in natural language, statements in computer science, and the ultimate method in evaluating truth and validity. Logic is not always intuitive to people, so we formalize it and explain it in a way to help organize your arguments and determine whether a conclusion really follows its premises.

Propositions

A proposition is any statement that can be true or false. In English, these are declarative sentences. The following are examples of propositions.

1. Mary has a sister.
2. It is raining outside.
3. I want carrots and peas.

A proposition is not a question or command. The following are not examples of propositions.

• Leave!
  • This is a command. It cannot be true or false.
• Do you have any pets?
  • This is a yes-no question. It would be odd to respond to this question as "true".
• Why don't you put the pen on the counter?
  • This is a wh-question. We respond with a reason rather than a simple "true" or "false".

We often formalize propositions with capital letters like P, Q, R, and so on.

• M = Mary has a sister.
• R = It is raining outside
• Q = I'm hungry.

If a proposition is true we write val(P) = 1. If a proposition is false we write val(P) = 0.