Asked by Tripp Hardee on May 20, 2024
Verified
Prove the following claim:
A disjunction with one tautological disjunct must itself be a tautology.
Disjunction
A logical operation that yields a true statement if at least one of its component statements is true.
Tautological Disjunct
A component of a logical statement that repeats the same information in different words, making it unconditionally true.
Tautology
A statement in logic that is true in every possible interpretation or a redundant statement that does not add new information.
- Digest the fundamentals of tautology, self-contradiction, and contingency within the framework of logical propositions.
- Verify the truth of logical statements comprising equivalences, disjunctions, and implications.
Verified Answer
MT
Michael TinglinMay 22, 2024
Final Answer :
The tautological disjunct will be true on every combination of truth values of its atomic components.Hence, regardless of the truth value of the other disjunct, the disjunction itself will be true on all truth value assignments of the atomic components.Therefore, the disjunction is a tautology.
Learning Objectives
- Digest the fundamentals of tautology, self-contradiction, and contingency within the framework of logical propositions.
- Verify the truth of logical statements comprising equivalences, disjunctions, and implications.