To add to Chris Hook's detailed explanation of the basics of propositional calculus there are certain names for each truth functor, used specifically in maths for computing.

**Conjuction** (^) also known as AND.

**Disjunction** (v) also known as OR.

**Implication** (→) also known as IF,THEN.

**Logical Implication** (↔) also known as IF and ONLY IF.

The more obvious one: **Negation** (¬) is NOT.