MATH135 Study Guide - Midterm Guide: Logical Connective, Mathematical Object, Riven

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Mukto Akash

Document Summary

A proof is a rigorous, formal argument that establishes the truth of a statement: a proof is a series of convincing arguments that leaves absolutely no doubt that a given proposition is true, or false. Objectives: define statement, proposition and axioms, develop a notion of proofs as convincing arguments that verify propositions. Definitions: statement: a sentence that has a definite state of being either true or false. Example: for every real number x, x2 + 1 > 2x: theorem: a particularly significant proposition, lemma: a subsidiary proposition. Objectives: define and, or, not using truth tables, evaluate logical expressions using truth tables, use truth tables to establish the equivalence of logical expressions, prove de morgan"s laws. A compound statement is a statement composed of several individual statements called component statements. Example: the statement ( is a real number) and (4=4) contains two component statements: is a real number, 4=4.