# CHAP 1. The Foundations: Logic & Proofs

## §1.1 Propositional Logic

◼ Proposition

Def. (Proposition)

A **proposition** is a declarative sentence that can be determined either *TRUE* or *FALSE*.

__Example__ of Propositions

- Seoul is the Capital of South Korea.
- 1+1=5
- 2⋅2=4

Non-propositional sentences

- x+1=32
- Read the book at night

Def. (Propositional variable)

A variable that represents a proposition.

__ Example __ of propositional variables

- p: Seoul is the Capital of South Korea.
- q: 1+1=5

Def. (Negation)

p: a proposition

The *negation* of p is the statement “It is not the case of p“.

We denoete it by ¬p.

__ Example__