Venn Diagrams John Venn Invented Venn diagrams as

Venn Diagrams

John Venn • Invented Venn diagrams as a way of picturing relationships between different groups of things.

How to Create a Venn Diagram • To draw a Venn diagram, you first draw a rectangle which is called your universe. It represents everything you’re dealing with right now. • Let’s say we wanted to create a Venn diagram for the universe of movie genres. If we wanted to classify movies as being either dramatic or comedic, we would draw circles to display our classifications. Movie Genres Dramatic Comedic

What are some movies that you consider to be only dramatic? What are some movies that you consider to be only comedic? Are there any movies that you consider to be both? Movie Genres Dramatic Comedic

Place the Numbers on the Venn Diagram

Set Notation Example • Let's say that our universe contains the numbers 1, 2, 3, and 4; that is, U = {1, 2, 3, 4}. U A • Note: The curly braces are the customary notation for sets. Do not use parentheses or square brackets. • Let A be the set containing the numbers 1 and 2; that is, A = {1, 2}. • Let B be the set containing the numbers 2 and 3; that is, B = {2, 3}. 1 B 2 4 3

Set Notation U: Universe (or Universal Set) U A U B A U A B U B A B

Cont. • Then we have the following relationships, with pinkish shading marking the solution "regions" in the Venn diagrams:

Practice Identify the shaded region using set notation.

Practice •

Interactive • http: //nlvm. usu. edu/en/nav/frames_asid_153_g_2_t_1. html? open=i nstructions&from=category_g_2_t_1. html

Answer the Questions Based On Venn Diagrams

Ex: Out of 40 students, 14 are taking English Composition and 29 are taking Chemistry. a) If five students are in both classes, how many students are in neither class? b) How many are in either class? c) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class? 2 38

Ex: A class of 35 students were surveyed and asked if they ever had dogs or cats for pets at home. 18 students said they had a dog. 16 students said they had a cat. 4 students said they have both a cat and a dog. a) How many students said they had never had a dog or a cat? Answer: 5 b) What is the probability that a randomly chosen student has only a cat?

Ex: https: //www. youtube. com/watch? v=U-Ov. L 3 Xl. Qw. Y

Ex: Draw a Venn Diagram which divides the twelve months of the year into the following two groups: Months whose name begins with the letter “J” and Months whose name ends in “ber”. Since the sets do not have any common elements, they are called disjoint sets (or mutually exclusive).

On Your Own: 150 college freshmen were interviewed. 85 were registered for a Math class. 70 were registered for an English class. 50 were registered for both Math and English. 35 a) How many signed up only for a Math Class? b) How many signed up only for an English Class? c) How many signed up for Math or English? 20 105 d) How many signed up neither for Math nor English? 45