Asked by Sarina Kumar on May 10, 2024
Verified
Prove the following claim:
If p q is a tautology, then p and q are equivalent statements.
Tautology
A statement or formula that is true in every possible interpretation, an irrefutable assertion.
Equivalent Statements
Phrases or sentences that express the same idea or proposition in different words.
- Demonstrate the validity of assertions that involve equivalences, disjunctions, and implications.
- Comprehend the association between logical propositions and their implications regarding consistency and equivalence.
Verified Answer
ZK
Zybrea KnightMay 13, 2024
Final Answer :
Suppose p q is a tautology.Hence, p q is true on all truth value assignments of the atomic components.So, for any given truth value assignment of the atomic components, either both p and q are true, or both p and q are false.Thus, for any given truth value assignment of the atomic components, p and q have the same truth values.Therefore, p and q are equivalent statements.
Learning Objectives
- Demonstrate the validity of assertions that involve equivalences, disjunctions, and implications.
- Comprehend the association between logical propositions and their implications regarding consistency and equivalence.