Discrete Mathematics and Its Applications | 1 CHAPTER The Foundations: Logic and Proofs | 1.3 Propositional Equivalences

DEFINITION 1

A compound proposition that is always true,no matter what the truth values of the proposi-tional variables that occur in it, is called atautology.

A compound proposition that is always false iscalled a contradiction.

A compound proposition that is neither a tautology nor a contradiction is called contingency.

 

Logical Equivalences

Compound propositions that have the same truth values in all possible cases are called logically equivalent.

 

DEFINITION 2

The compound propositions p and q are called logically equivalent if p ↔ q is a tautology.

The notation p ≡ q denotes that p and q are logically equivalent.

 

 

 

 

 

 

 

 

 

 

In general, 2**n rows are required if a compound proposition involves n propositional variables.