# Boolean Logic Index

Boolean Logic is a branch of mathematics operates on true and false values. It is used to implement computer hardware and in programming languages.

## Notation

The "and" operator is denoted with the carrot symbol, which looks like a equilateral triangle with no bottom side. The operator evaluates to true if both the left and right expressions are true, otherwise evaluates to false.

Two stacked horizontal lines respresents the equals symbol in mathematics. The two expressions on either side are equal, or the same, when the equal sign is placed in between them.

The logical or symbol describes when either one thing is true, the other thing is true, or both is true.

The equivalent operator is used to express that two expressions are equivalent, although not necassarily equal.

The boolean operator for implication is denoted using a double arrow pointing to the right.

The negation symbol is used to reperesent the unary operator for negation, which inverts the value of the expression it is applied to.

Xor is the boolean operator that describes the operation of exclusive or. For example, when a waiter asks whether you want orange juice or coffee, they are really asking an exclusive or: you can have one or the other, but not both.

## Operators

The logical and operator returns true if both the left side expression and the left side expression evaluate to true, otherwise the operator returns false.

The logical exclusive or (abreviated as xor) operator returns true if the left side evaluates to true and the right side evaluates to false. The operator also returns true if the left side evaluates to false and the right side evaluates to true. Otherwise, returns false.

The logical if and only if operator, or iff for short, returns ture

The logical implication operators returns true if the left and right hand side expressions evaluate to true, or if the left-hand expression is false.

The logical "or" operator returns true if either the left side expression evaluates to true or the right side expression evaluates to true, otherwise returns false.