3.1 Review a) Draw a Venn diagram to show: The universal set, U = {natural numbers from 1 to 40}; E = {multiples of 3}; F = {multiples of 15} ; S = {multiples of 9}. b) List the disjoint subsets, it there are any. c) Is each statement true or false? Explain. i. E is a subset of F. ii. S is a subset of E. iii. S is a subset of F. iv. F’ = {all numbers from 1 to 40, except 15 and 30}. v. S is a subset of S

3.2 Review 1. A total of 20 students are on a field trip. Of these students, 13 are wearing sunglasses and 6 are wearing a hat. Only 5 students are not wearing sunglasses or a hat. (a) How many students are wearing both sunglasses and a hat? (b) How many students wearing sunglasses but not a hat? (c) How many students are wearing a hat but not sunglasses?

3.2 Review 2. Jordan asked 40 students at his school cafeteria what they bought for lunch. He recorded his results in the table below. PurchaseNumber of Students Beverage34 Soup18 No Beverage nor Soup5 Let’s draw a Venn diagram. Then answer the following: a) How many students bought a beverage and soup? b) How many students bought only a beverage or only soup?

3.3 Review 1. Paul asked 20 students whether they have a dog or a cat. – 4 students do not have a dog or a cat – 8 students have a dog – 8 students have a cat How many students have both a dog and a cat?

Memory Trick the difference between ‘or’ and ‘and’. “Or”“And” Union: “Is my element in set A OR set B?” If yes, then it is a part of A B. for ‘union’. Intercept: “Is my element in set A AND set B?” If yes, then it is a part of A B. looks like a capital ‘A’ for ‘and’.

3.3 Review 2. Consider these two sets: A = {-12, -9, -6, -3, 0, 3, 6, 9, 12} ; B = { x | -12 ≤ x ≤ 12, x is an element of I } a) Determine A union B, and the number in the set. Determine A intersect B, and the number in the set. b) Draw a Venn diagram to show these two sets

3.3 Review 3. Neil asked 40 people at a bookstore if they prefer romance novels or horror novels. 18 people do not like either. 10 people like romance novels. 13 people like horror novels. Determine how many people like both romance and horror novels.

Your Turn Please complete on a separate piece of paper: Make a list of objects that relate to a subject of your choice – (e.g. a list of different sports equipment, a list of positions in a sport, a list of characters from your favorite TV show or movie, a list of your favorite food, etc.) Categorize your list into two (or more) groups. Draw a Venn Diagram, and fill in numbers using your list.

Miss. Pravda’s Turn

The Galactic Republic and the Sith are having a battle on Naboo. There are 150 storm troopers, Darth Maul, Darth Tyranus, Boba Fett, Obi Wan Kenobi, Anakin Skywalker, 5 wookies, Qui-Gon Jinn, C-3PO,and R2-D2. Create a Venn diagram to show: - the number of republicans, - the number of sith members, - the number of people using guns, - the number of people using lightsabers. RepublicSith Obi Wan Kenobi (1), Anakin Skywalker (1), Qui-Gon Jinn (1), C-3PO (1), R2D2 (1), Wookies (5) Darth Maul (1), Darth Tyranus (1), Boba Fett (1), Storm Troopers (150) Draw a Venn Diagram including the numbers from this example.

Republic Sith Lightsabers Guns

3.4 Applications of Set Theory

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Example 1:

Example 2:

Principle of Inclusion and Exclusion continued: When we only had two sets: Now that we have three sets:

Assignment: Point to Ponder: “If you consider the set of all sets that have never been considered, will it disappear?” Page 191 # 2,4,6,9,12