MATE 3314 Week 4-Logical Equivalence Properties.b.pptx -...

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Section 05 Logical EquivalencePropertiesMATE 3314 Fundamentals of Mathematical Structures and ProcessesSpring 2021Dr. Aaron T Wilson
The following are logical equivalences that are so important to thefield of logic that they are calledLaws. You should know these.(In the following,TandFrepresent propositions that are alwaysTrueor alwaysFalse, respectively. Hence, Tautologies andContradictions.)Identity lawsNegation lawsCommutative laws•Associative lawsDistributive lawsDouble negation lawDeMorgan’s laws
Example 1Use DeMorgan’s laws to find a statement that is logically equivalent tothe negation of the following statement:“Line m is parallel to line n or line m is perpendicular to line n.”DeMorgan’s laws
Definition: theDualof a propositionAnother important concept in logic concerns the “dual of a proposition”. We can thinkabout the dual like a kind of partner of a given proposition. And we define it this way:Thedualof a proposition that contains only the operators~, ,andis the

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Logic, equivalences, Dr Aaron T Wilson, Mathematical Structures and Processes, Dual of a proposition

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