What is a Proposition?

A statement that can be true of false.

Examples:

1. sqrt(2) is irrational.
2. 1+1=5
3. The tiger will become extinct before the Gorilla on the planet Earth.
4. Socrates was left handed.

Main Points:

1. Difficulty of establishing the actual (realworld) truth value is unimportant
2. Some values can be immediately computed as T or F #1 or #2, others may take many years #3 or we may never know #4.

Non-Proposition Examples:

1. Can you please pass me the Ketchup?
2. x^2 = 49
3. This sentence is false.

Main Points:

1. Interrogative statements are neither T nor F.
2. #2 may be T or F depending on the value assigned to x.
3. Neither T nor F - a paradox.

Atomic Propositions - do not contain any other propositions - ex: It is raining. 

Compound Propositions - are formed by combining logical connectives with atomic (simple) propositions - ex: I am drinking coffee and its raining outside.