I&C SCI 6B Chapter Notes - Chapter 1.3: Associative Property

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

Document Summary

Textbook used: discrete mathematics and its applications, rosen, 7th edition. Tautology: a compound proposition that is always true, no matter what the truth values of the propositional variables that occur in it. Example: p (cid:1319) p is always true, so it is a tautology. Contradiction: a compound proposition that is always false. Example: p (cid:1318) p is always false, so it is a contradiction. Contingency: a compound proposition that is neither a tautology or contingency. Definition: the compound propositions p and q are called logically equivalent if p q is a tautology. The notation p q denotes that p and q are logically equivalent. Use a truth table to determine if compound propositions are equivalent. P1 (cid:1319) p2 (cid:1319) p3 (cid:1319) pn and p1 (cid:1318) p2 (cid:1318) p3 (cid:1318) pn are well defined whenever p1, p2, pn are propositions. Tells us how to negate conjunctions and disjunctions >> flip ands and ors.