MACM 101 Lecture 10: Lecture 10
13 Aug 2016
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Simplify so that the negations are attached only to propositional variables. When simplifying, it is usually a good idea to get all negations attached only to propositional variables. It always pays to expand the outermost bracket first. Definition: let s represent a logical expression composed of propositional variables, t0, f0, , (cid:2396), (cid:2395). The dual of s (denoted sd) is the statement obtained by transforming all: Let s and t be propositional defined as above. Observe that the laws of logic come in pairs, which are the duals of each other. Therefore, if we are forced to prove the laws of logic, our work would be cut in half if we prove the first of each pair (by truth table) and invoke the principle of duality! Definition: a predicate (or propositional function or open statement) contains at least one variable which, upon substitution, transforms the predicate into a proposition (with no variables)
