PROPOSITIONAL EQUIVALENCES

Before we proceed, we must first understand the terms and operators used in this topic.

   

PROPOSITION is the statement that 
is either true or false.
        

COMPOUND PROPOSITION is the 

statement that is formed using 
logical operators.

Propositional Equivalences

Tautology is compound proposition that is always true.

p	¬p	p v ¬p
TRUE	FALSE	TRUE
FALSE	TRUE	TRUE

Contradiction is compound proposition that is always false.

p	¬p	p Λ ¬p
TRUE	FALSE	FALSE
FALSE	TRUE	FALSE

Contigency is proposition that is neither tautology nor contradiction.

Logical equivalent: two compound propositions that have the same truth value.

Example:

If it rains then I stay at home.

If I do not stay at home, then it does rain.

Applications of logical equivalent are:

•  De Morgan Law
•  Distributive Law