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