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.