Propositional Calculus

Introduction

Moving on forward, after establishing that math is a language and learning the basics, we now discuss propositional calculus.

What is propositional calculus? In simple terms, it is the relationship of statements to figure out their relationship. Recollect your knowledge from the previous lesson as we are about to use those in this part of the lesson.

Tautology, Contradiction, and Contingency

For this section of Propositional Calculus, we’ll discuss logical equivalences. Mainly tautology, contradiction, and contingency. These worlds may look intimidating, but they’re actually very easy to understand.

Simply, tautology is when all entries in the column of a truth table are true. 

Similarly, contradiction is when all entries in the column of a truth table are false. 

On the other hand, contingency is when the data set is neither all true nor all false.

Given the previous example in the video lecture:

As you can see, in the 4th column, all of it has T values, therefore, it is a tautology.

On the hand, the 7th column contains all F values, therefore, it is a contradiction.

Finally, in the 8th column, it is all neither all T nor F, therefore, it is a contingency.