MATH 1P66 Lecture Notes - Lecture 4: Universal Quantification, Existential Quantification, Propositional Function

• School: Brock University
• Department: Mathematics and Statistics
• Course: MATH 1P66
• Professor: Basil Nanayakkara

Document Summary

#16 b) prove t or f (p q) ^ (q r) (p r) remember: p q = q v p. = rv p v [(qv p)^(rv q)] remember: (p^q) = p v q. = rv p v (qv p) ^ (rv q) disjunctions so one unit. = rv( p v (qv p)) v (rv q) de morgan"s law to next line. = rv[ p v ( q^p)] v (rv q) distributive. Negation of q, or negation of p and q. = [(pvq)^(p r)^(q r)] r. = rv [(pvq) ^ [rv (pvq)]] let t = pvq. = rv tv (rv t) basically pv p let s= rv t. A propositional function is much like an algebraic function f(x) = x^2 domain is r set of real # You put an input you get an output. P(x): 9-x^2>0 not a proposition domain = z set of all integers. Insert something for x you get a proposition.