Disjunction
PvQ . Only false if both P and Q are false. Otherwise, true.
Conjunction
P^Q . Only true if both P and Q are true.
Conditional
P -> Q . If P, then Q. P is called the antecedent and Q is called the consequent. Only false id P is true and Q is false. Otherwise, it is true.
Biconditional
P<->Q . P if and only if Q. The sentence is true when the truth value for P is the same as the truth value for Q.
Totalogy
Everything is true
Contradiction
Everything is false
Contingent
Mix of true and false
Equivalent
If two propositions are the same
Consistent
If two propositions can be true at the same time
Inconsistent
If two propositions match, but only false