Given the statements p and q, an implication is a statement that is false when p is true and q is false, and true otherwise.
A biconditional statement is true whenever the truth value is the same for both p and q and false otherwise.
'AND:' Given p and q, a conjunction is the proposition that is true when both p and q are true and is false otherwise.
'OR:' Given p and q, a disjunction is the proposition that is false when both p and q are false, but is true otherwise.
'XOR:' An exclusive or is a proposition which is true when exactly one of p and q is true and is false otherwise.
The universal quantification of P(x) is the proposition "P(x) is true for all values x in the universe of discourse."