In discrete mathematics, tautology, contradiction, and contingency are important concepts that are used to evaluate the truth or falsity of logical statements.
A tautology is a statement that is always true, regardless of the truth values of the propositions it contains. For example, the statement "A or not A" is a tautology because it is true regardless of whether A is true or false.
On the other hand, a contradiction is a statement that is always false. For example, the statement "A and not A" is a contradiction because it is impossible for A to be both true and false at the same time.
Lastly, a contingency is a statement that is neither a tautology nor a contradiction. It's a statement that is true or false depending on the truth value of the propositions it contains. For example, the statement "If it rains, I will take an umbrella" is a contingency because it is true if it rains, and false otherwise.
In this video, we will explore these concepts in more detail, including examples and exercises to help you understand and apply them in your own work. We will also discuss how these concepts are used in the field of logic, including in the evaluation of logical arguments and in the design of digital circuits.
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