LESSON 01 – INTRODUCTION TO LOGIC

LESSON NOTE

TERMINOLOGY

• A Boolean value is a value that can be either true or false.
  
  
• A Boolean statement is a statement that is either true or false.

Ex1: The world is flat. – false

Ex2: Mr. Campeau is cool. – true

WHY CARE?

· So why in the world are we looking at this?

Answer: true = 1, false = 0 (this is binary with different symbols)

· Boolean operators join Boolean statements together. The common ones are AND and OR.

· A Boolean expression is the combination of Boolean statements (or values) joined together by Boolean operators.

Ex: Canada’s capital is Ottawa AND Ontario’s capital is Toronto

· AND – The overall statement is true only if both individual statements are true.

Ex:

Earth is a planet AND Canada is a continent. (true AND false = false)

Ravioli is pasta AND apples are fruit (true AND true = true)

· OR – The overall statement is true as long as at least one statement is true.

Ex:

Oranges are vegetables OR corn is yellow (false OR true = true)

Red is a colour OR the Sun is a star (true OR true = true)

· Another operator is NOT. It only deals with a single statement and inverses the Boolean value of that statement.

Ex:

An orange is a fruit. (True)

An orange is NOT a fruit. (False)

· The above rules can be explained in truth tables.

Table for AND:

Statement 1	Statement 2	Result
True	True	True
True	False	False
False	True	False
False	False	False

Table for OR:

Statement 1	Statement 2	Result
True	True	True
True	False	True
False	True	True
False	False	False

Table for NOT

Statement 1	Result
True	False
False	True

Note: True could be replaced by 1. False could be replaced by 0.

In fact, in future lessons, we will be placing 0s and 1s inside truth tables instead.