Compound Proposition in Discrete Mathematics
A proposition consisting of only a single propositional variable or a single propositional constant is called an atomic proposition or simply proposition that can not be further subdivided. A proposition obtained from the combinations of two or more propositions using logical operators or connectives of two or more propositions or by negating a single proposition is referred to as molecular or composite or compound proposition.
The words and phrases or symbols used to form compound propositions are called connectives. There are five basic connectives called Negation, Conjunction, Disjunction, Implication or Conditional and Equivalence or Biconditional. The following symbols are used to represent connectives.
If p is any proposition, the negation of p is denoted by ~p and read as not p. It is a proposition which is false when p is true and true when p is false. Consider the statement:
p: Paris is in France.
Then the negation of p is the statement
~p: It is not the case that Paris is in France.
Normally, it is written as
~p: Paris is not in France.
Strictly speaking, not is not a connective, since it doesn’t join two statements and ~p is not really a compound statement. However, not is a unary operation for the collection of statements, and ~p is a statement if p is considered a statement.