Tautologies and Fallacies With Example

Basic Concept Of Tautologies and Fallacies

Tautologies or theorems are like axioms which are true for all values. In a truth table of tautology there will be only T in the last column. For example p OR~p= p, p AND p=p, and ~ ~p=p are all tautologies. As against these the Fallacies are the contradictions which will never be truth and obviously there will be only F in the output column of a truth table. For example p AND ~p is a contradiction, how can a statement and its negative both be true. These truth tables will further reveal this fact.

Since tautology is always true its negation is a fallacy and is always false.

• Example 1: Verify the following statement by constructing truth tables:

 

Solution:
(i)

Since there is T for all values of p, q in column 5, it is a tautology.

(ii)

Since there is F all values of p, q in column 6, it is a Fallacy

• Example 2: Using truth tables, show that (p AND q) =p, and p = (p OR Q) are both tautologies, where p,q are any two statements.

 Solution : 

Since all the entries in column 4 and 6 are T, the given proposition is both tautologies.