# Propositional Logic

## Introduction to Logic

Logic defines a formal language for representing knowledge and for making logical inferences. It helps us to understand how to construct a valid argument.

Logic defines:
- Syntax of statements
- The meaning of statements
- The rules of logical inference (manipulation)

### Propositional Logic

Definition: A proposition is a statement that is either true or false.

Examples:
- Dubai is the capital city of UAE.
*Answer*: False.
- 3 + 4 = 7.
*Answer*: True.
- How are you today?
*Answer*:A question is not a proposition.
- x + y = 3
*Answer*: It is neither true nor false.

### Composite Statements

More complex propositional statements can be build from elementary statements using logical connectives.

Examples:
- Proposition A: ″ It is sunny today″
- Proposition B: ″We will go to the park″
- A new (combined) proposition:″If it is sunny today then we will go to the park″

### Logical connectives

- Negation
- Conjunction
- Disjunction
- Exclusive
- Implication
- Biconditional

#### Negation

Definition: Let p be a proposition. The statement ″It is not the case that p.″ is another proposition, called the negation of p. The negation of p is denoted by ¬p and read as "not p″.
Examples
- Pasadena is located in the State of California. The negation of this statement is:

It is *not the case*that Pasadena is located in the State of California.
- 15 is
*not* a prime number.

Exercise: Negate the following propositions:
- It is sunny outside. Answer: It is
*not* sunny outside
- 3 is a prime number. Answer: 3 is
*not* a prime number
- Spain is in Europe. Answer: Spain is
*not* in Europe.

For more details, please contact me here.

Date of last modification: February 27, 2019