MATH 200 Lecture Notes - Lecture 1: Gie, Propositional Calculus, Propositional Formula

• School: Truman State University
• Department: Mathematics
• Course: MATH 200
• Professor: Easley

Document Summary

This sentence is false (this is a false statement) The above truth table of an or proposition is equivalent with the bottom. Equivalent propositional forms: always true is called tautology. I. e. gi(cid:448)e(cid:374) a truth ta(cid:271)le i(cid:374) (cid:374) propositio(cid:374)al (cid:448)aria(cid:271)les, p(cid:1005), p(cid:1006), p(cid:1007), , can we find a propositional formula (cid:894)usi(cid:374)g p(cid:1005), p(cid:1006), p(cid:1007), , p(cid:374), ~, v, a(cid:374)d (cid:895) Can we find a propositional equation that will give a tautology no matter what the inputs are, only using. It will end up being a very long string of or statements. P is called the antecedent, and q is called the consequent. P v q = q v p commutative laws. Q p = p q co(cid:373)(cid:373)utati(cid:448)e la(cid:449)s. P v (q v r) = (p v q) v r associative law. P (cid:894)q v r(cid:895) = (cid:894)p q(cid:895) r asso(cid:272)iati(cid:448)e la(cid:449) P (cid:894)q v r(cid:895) = (cid:894)p q(cid:895) v (cid:894)p r(cid:895) distri(cid:271)uti(cid:448)e la(cid:449)s.