CSCE 235

Handout 2: Propositions

January 12, 2004

Propositional calculus is the study of the logical relationship between objects called propositions. A proposition will be any sentence that is either true or false, but not both. We do not need to know what its truth value is in order to consider a proposition.

A proposition is a statement, not a question.

Connectives

Propositions can be combined to obtain compound propositions using standard connective symbols:

Operators	Meaning
	“not” or negation
	“and” or conjunction
	“or” [inclusive] or disjunction
	“or” [exclusive], either or, cannot be both
	“implies” or the conditional implication
	“if and only if” or the biconditional:

Definitions

reads

· p implies q

· if p then q

· p only if q

· q if p

· p is a sufficient condition for q

· q is a necessary condition for p

· if p then q

· if p, q

· p is sufficient for q

· q when p

· q whenever p

· q is necessary for p

· q follows from p

reads

· p if and only if q

· p is necessary and sufficient for q

· if p then q, and conversely

· p iff q

The proposition is called the converse of the proposition .

The contrapositive of the proposition is .

The inverse of the proposition is .