Reasoning and Logic

Day 4: Venn Diagrams & Applications

Today's Objectives

Define and identify parts of a Venn diagram.
Connect Venn diagrams to the logical operators AND & OR.
Represent and interpret data using Venn diagrams.

Warm-Up: Sorting Groups

Think about the students in this class.

List two groups you could sort students into.
Can a student be in BOTH groups?
Can a student be in NEITHER group?

What is a Venn Diagram?

A diagram that uses circles to show relationships between sets of items.

Key Vocabulary

Universal Set (U): The rectangle containing everything.
Intersection (A ∩ B): The overlap. Items in A AND B.
Union (A ∪ B): Everything in the circles. Items in A OR B.
Complement (A'): Everything NOT in A.

Example: How to Fill It In

25 students: 15 like Soccer (S), 12 like Basketball (B), 7 like both.

Start with BOTH (Intersection): 7
Soccer ONLY: 15 - 7 = 8
Basketball ONLY: 12 - 7 = 5
NEITHER: 25 - (8+7+5) = 5

Guided Practice

50 people: 30 own a dog (D), 22 own a cat (C), 10 own both.

Where do we start?
How many own ONLY a dog?
How many own ONLY a cat?
How many own neither?
How many own a dog OR a cat?

Independent Practice

Choose your level and solve the problems.

RED

Use diagram: 10 in Band only, 5 in both, 12 in Chorus only.
1. How many in Band?
2. How many in Chorus?
3. How many in Band AND Chorus?

YELLOW

30 students: 18 like vanilla, 14 like chocolate, 6 like both.
1. Draw the diagram.
2. How many like ONLY vanilla?
3. How many like neither?

GREEN (Challenging)

Out of 50 people, 20 use Netflix, 18 use Hulu, and 22 use Disney+. 7 use N & H, 9 use N & D+, and 6 use H & D+. 3 people use all of them.
1. Draw the diagram.
2. How many people used Netflix and Hulu?
3.How many people used none of these services?

Exit Ticket

On your notecard:

20 customers were surveyed. 13 own a dog. 9 own a cat. 5 own both.

1. Draw a Venn diagram to represent this.

2. How many customers own neither a dog nor a cat?

Geometry Presentation