PROPOSITIONAL LOGIC

• Definition: A proposition is a declarative sentences that is either true or false.

• Example: X + 2 = 5

• Truth Table:

 NEGATION 

P	¬ P
TRUE	FALSE
FALSE	TRUE

CONJUNCTION

P	Q	P ˆ Q
TRUE	TRUE	TRUE
TRUE	FALSE	FALSE
FALSE	TRUE	FALSE
FALSE	FALSE	FALSE

DISJUNCTION

P	Q	P  ˇ  Q
TRUE	TRUE	TRUE
TRUE	FALSE	TRUE
FALSE	TRUE	TRUE
FALSE	FALSE	FALSE

EXCLUSIVE DISJUNCTION

P	Q	P     Q
TRUE	TRUE	FALSE
TRUE	FALSE	TRUE
FALSE	TRUE	TRUE
FALSE	FALSE	FALSE

IMPLICATION

P	Q	P            Q
TRUE	TRUE	TRUE
TRUE	FALSE	FALSE
FALSE	TRUE	TRUE
FALSE	FALSE	TRUE

BI-IMPLICATION

P	Q	P              Q
TRUE	TRUE	TRUE
TRUE	FALSE	FALSE
FALSE	TRUE	FALSE
FALSE	FALSE	TRUE