MAT 137 LEC 0601 Instructor: Alessandro Malus TA: Muhammad Mohid - PowerPoint PPT Presentation

MAT 137 — LEC 0601 Instructor: Alessandro Malusà TA: Muhammad Mohid September 15th, 2020 Warm-up question : Call M the set of all members of a family, and T the set of toothbrushes in their bathroom. Which of the following do you expect to be true? 1 ∀ m ∈ M , ∃ t ∈ T such that m brushes their teeth with t ; 2 ∃ t ∈ T such that ∀ m ∈ M , m brushes their teeth with t .

Sets and quantifiers What are the following sets? 1 A = { x ∈ R : ∀ y ∈ [0 , 1] , x < y } 2 B = { x ∈ R : ∃ y ∈ [0 , 1] s.t. x < y } 3 C = { x ∈ [0 , 1] : ∀ y ∈ [0 , 1] , x < y } 4 D = { x ∈ [0 , 1] : ∃ y ∈ [0 , 1] s.t. x < y } 5 E = { x ∈ [0 , 1] : ∃ y ∈ R s.t. x < y } 6 F = { x ∈ [0 , 1] : y ∈ R , x < y }

Negation Write the negation of these statements as simply as possible: 1 My favourite integer number is greater than 7. 2 I know at least five students at U of T who have a cellphone. 3 There is a country in the European Union with fewer than 1000 inhabitants. 4 All of my friends like apples. 5 I like apples and oranges. Negation of · · · = · · · is false.

Before next class... • Watch videos 1.7, 1.8, and 1.9. • Download the next class’s slides (no need to look at them!) Note : Office hours are now available! See them at http: //www.math.toronto.edu/alfonso/137/137.html?officehours