Contradiction truth table

A proposition is a statement that can either be true or false and cannot hold a neutral or indeterminate value. For example, the statement "2 + 3 = 5" is a true proposition because the mathematical expression evaluates to the correct result of 5.

What is a contradiction?

A contradiction is a proposition that is always false, regardless of the truth and false values of the individual propositions that produce the result. This concept is useful in mathematics and sciences to help us identify errors, inconsistencies, and conflicts in our data.

Truth table examples

Let's discuss some examples of contradiction: one and two propositions.

Using one proposition

Let's understand contradiction with an easy example involving just one proposition: m. In the following table, we calculate the negationIt returns result opposite to the input condition. of the proposition represented as ∼m. Then, we take ANDIt returns true if all input conditions are true else false for all cases. of m and ∼m represented as m ∧ ∼m.

Note: Here T refers to true while F refers to false.

We conclude that m ∧∼m is a contradiction as it results in all false outputs.

Two propositions

Let's dive deep into the contradiction concept now involving two propositions: m and n. We want to calculate ∼m ∧ (m ∧ n), so we find ∼m and m ∧ n individually first. Then, we take the AND between them to get our desired output.

We conclude that ∼m ∧ (m ∧ n) is a contradiction as it results in all false outputs.

Conclusion

Contradictions play an important role in various areas of science. They help us find errors, maintain accuracy, and improve the quality of our systems. Contradictions can help us find potential errors and shortcomings in our system so we can fix and improve it accordingly.

Let's test what we have learned so far.