What is the contingency 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 "10 + 4= 14" is a true proposition because the mathematical expression evaluates to the correct result of 14.

What is a contingency?

A contingency is a proposition that has both true and false values in its output. It is neither a contradictionAll the output values are false. nor a tautology.All the output values are true. This concept is useful in mathematics and sciences in reasoning, decision-making, risk management, and problem-solving.

Truth table examples

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

Using one proposition

Let's understand contingency 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.

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

We conclude that ∼m is a contingency as it results in output with both true and false values.

Two propositions

Let's dive deep into the contingency concept now involving two propositions: m and n. We want to calculate ∼m ∨ (m ∧ n), so we find ∼m first. Then we find the ANDIt returns true if all input conditions are true else false for all cases. between m and n represented as m ∧ n. Lastly, we take the OR It returns true if atleast one of the input condition is true.between them to get our desired output.

We conclude that ∼m ∧ (m ∨ n) is a contingency as it results in output with both true and false values.

Conclusion

Contingency plays an important role in various areas of science. It helps us make predictions based on different conditions. We get outcomes that have true and false both values for different cases, which helps in dealing with uncertainties and decision-making.

Let's test what we have learned so far.