Tautology Definition 37D296
1. The problem asks to identify the correct definition among the given options about logical statements.
2. Let's review the definitions:
- A tautology is a statement that is always true, regardless of the truth values of its components.
- A contradiction is a statement that is always false, regardless of the truth values of its components.
- A statement that can be true or false depending on the values of its propositions is called a contingent statement.
3. Now, analyze each option:
- a. "A statement that is always false is called a tautology." This is incorrect because a statement always false is a contradiction, not a tautology.
- b. "A statement that is always true is called a contradiction." This is incorrect because a statement always true is a tautology, not a contradiction.
- c. "A statement that can be true or false depending on the values of its propositions is called a tautology." This is incorrect because such a statement is contingent, not a tautology.
- d. "A statement that is always true is called a tautology." This is correct.
4. Therefore, the correct definition is option d.
Final answer: d. A statement that is always true is called a tautology.