What is a Tautology in Logic?
A tautology is a logical statement that is always true, regardless of the truth values of its components. It is valid in every possible interpretation or scenario. Tautologies are important in logic because they reflect principles of logical necessity.
Symbolic Representation
One common tautology is: p ∨ ¬p
This reads as: “p or not p,” which is always true, no matter the truth value of p.
Truth Table
| p | ¬p | p ∨ ¬p |
|---|---|---|
| T | F | T |
| F | T | T |
Examples
1. “It will either rain or not rain.”
2. “All bachelors are unmarried.”
Conclusion
Tautologies are used to test the validity of arguments and prove logical truths. In logic, identifying tautologies helps in constructing sound and irrefutable arguments.