MATH135 Lecture Notes - Lecture 1: Ion, Contraposition, Vacuous Truth

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Gabrielde Morais Coutinho

Document Summary

University of waterloo - fall 2014 - math 135. A statement is a sentence that has a de nite state of being true or false. If a sentence does not have a de nite state of being true or false, then it is not a statement. Consider the examples below: is there an integer n such that 90 < n2 + 10 < 100 , find an x such that x2 4x + 3 < 0, n2 > m3. This last sentence becomes a statement if a de nite value is assigned to the variables n and: such sentences are called open sentences. 1. 3 exercise. (i) decide whether of not the statements in example 1. 2 are true or false. (ii) find values for n and m that make the open sentence n2 > m3 a true statement. Given a statement, it might not be obvious whether or not the statement is true or false.