I&C SCI 6B Lecture Notes - Lecture 3: Logical Reasoning

• School: UC-Irvine
• Department: Information and Computer Science
• Course: I&C SCI 6B
• Professor: Irani

Document Summary

Ics 6b lecture 3 logical equivalence and logical reasoning. Logical equivalence: compound propositions are logically equivalent if they have the same truth value for every combination of truth values for their individual propositions, two logically equivalent compound propositions may not necessarily have the same set of variables. De morgan"s law: ~(p ^ q) ~p v ~q, ~(p v q) ~p ^ ~q. Conditional identity: p -> q ~p v q. Tautologies are propositions that evaluate to true for every truth assignment to its variables: tautologies are logically equivalent to true, to disprove a tautology, show one truth value for the variables to show the proposition evaluates to false. Contradictions are propositions that evaluate to false for every truth assignment to its variables: contradictions are logically equivalent to false, to disprove a contradiction, show one truth value for the variables to show the proposition evaluates to true.