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Chapter 3: Problem 93

What is the difference between a tautology and a self-contradiction?

Short Answer

Expert verified
The difference between a tautology and a self-contradiction lies in their truth values. A tautology is a compound proposition that is always true regardless of the truth values of its individual propositions, representing a rule of logic. On the other hand, a self-contradiction is a compound proposition that is always false, no matter what the truth values of its constituent propositions are.

Step by step solution

01

Definition of Tautology

A tautology in propositional logic is a compound proposition that is always true, regardless of the truth values of the individual propositions that constitute it. It signifies a rule of logic. For example, the compound proposition (P 鈭� 卢P) - meaning, 'P or not P' - is a tautology because it is always true, whether P is true or false.
02

Definition of Self-contradiction

A self-contradiction, or a contradiction, in propositional logic, is a compound proposition that is always false, no matter what the truth values of its component propositions are. For instance, the compound proposition (P 鈭� 卢P) - meaning, 'P and not P' - is a contradiction because it is always false, whether P is true or false.
03

Contrast between Tautology and Self-contradiction

The main difference between a tautology and a self-contradiction lies in their truth values. A tautology is a proposition that is invariably true while a self-contradiction is a proposition that is invariably false. They represent the two extremes of truth values for compound propositions in propositional logic.

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Most popular questions from this chapter

Determine whether each argument is valid or invalid. All \(A\) are \(B\), no \(C\) are \(B\), and all \(D\) are \(C\). Thus, no \(A\) are \(D\).

If you are given an argument in words that contains two premises and a conclusion, describe how to determine if the argument is valid or invalid.

Determine whether each argument is valid or invalid. No \(A\) are \(B\), some \(A\) are \(C\), and all \(C\) are \(D\). Thus, some \(D\) are \(B\)

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If I'm at the beach, then I swim in the ocean. If I swim in the ocean, then I feel refreshed. \(\therefore\) If I'm not at the beach, then I don't feel refreshed.

Use Euler diagrams to determine whether each argument is valid or invalid. All physicists are scientists. All scientists attended college. Therefore, all physicists attended college.
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