The predicate calculus has a number of theorems and axioms for proving logical statements. Here are the main symbols used in predicate calculus:
P(x)  proposition  a logical statement in the condition x.
x  any condition in the set of possible conditions.
c  a particular condition in the set of possible conditions.
"  "For every"
$  "Exists"
®  Implication
Ù  Conjunction (logical and)
Ú  Disjunction (logical or)