# Mathematical Logic

**Mathematical Logic** is a formalized method of analyzing situations.

Boolean Algebra is related to this topic.

Charts or tables are used with particular symbols for each of the operators.

A **statement** can only be true or false, it cannot be a question or command or anything similar.

- “the book is green” is a statement. It can only be true or false, it is not a command, a question or anything else.
- “Give me the book” is not a statement, it is a command.

Normally we represent statements with p, q, r, etc when we are workign to save space. It is reasonable to use other letters to represent the statement to help remember what it is representing. For example, g = the book is green would be reasonable.

Some of our **binomial operators** are AND, OR, XOR, NAND, and others. Binomial operators can only work with 2 statements at a time, similar to some of our arithmetic operators (+, -, …) Some of these are similar to the ones used in Sets (link to be added).

**NOT** is a single operator, it changes the truth value of the single input or statement.

**AND** the result is true if both statements are true.

**OR** the result is true if at least one of the statements is true.