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Thinking Critically

1B Discussion Paragraph

1 web 103. Web Searches

1 world 104. Logical Or 105. Multiple Negation 106. Conditional News

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Unit 1C

Sets and Venn Diagrams

1-C

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Definitions A set is a collection of objects.

The members of a set are the individual objects within it.

Write sets by listing their members within a pair of braces, { }.

Use three dots, …, to indicate a continuing pattern if there are too many members to list.

A Venn diagram is a diagram that uses circles to represent sets.

1-CSet NotationCN 1a-c

1. Use braces to write the contents of each of the following sets:

a. the set of countries larger in land area than the United States

b. the set of years of the Cold War, generally taken to have started in 1945 and ended in 1991

c. the set of natural numbers greater than 5

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1-C

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Set Relationships

If A is a subset of B, then all members of A are also members of B.

If A is disjoint from B, then the two sets have no members in common.

If A and B are overlapping sets, then the two sets share some of the same members.

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The set whales is a subset of the set mammals.

Venn Diagram for Categorical Propositions

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The set of fish is disjoint from the set mammals.

other animals

Venn Diagram for Categorical Propositions

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men who are not doctors

The sets of doctors and women are overlapping.

male doctors

female doctors

women who are not doctors

Venn Diagram for Categorical Propositions

1-CVenn DiagramsCN 2a-b

Describe the relationship between the given pairs of sets and draw a Venn diagrm showing this relationship. Interpret all the regions of the Venn diagram.

a. Democrats and Republicans (party affiliations) b. Nobel Prize winners and Pulitzer Prize winners

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1-CSets of NumbersCN 3

3. Draw a Venn Diagram showing the relationships among the sets of natural numbers, whole numbers, integers, rational numbers, and real numbers.

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Real Number Venn DiagramWhere are irrational numbers?

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All S are P

No S are P

Some S are P

Some S are not P

All soccer players are athletes.

No goalies are baseball players.

Some mathematicians are philosophers.

Some politicians are not men.

Categorical Propositions

1-CVenn Diagrams for Categorical PropositionsCN 4a-d

Draw a Venn diagram to represent each of the four sample propositions

a. All S are P b. No S are P c. Some S are P d. Some S are not P

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1-C

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Constructing a Venn Diagram

Statement: “Some dogs can swim.”

Rephrase to: “Some dogs are animals that can swim.”

Construct the Venn diagram:

1-CRephrasing in Standard FormCN 5a-b

5. Rephrase each of the following statements in one of the four standard forms for categorical propositions, then draw the Venn diagram.

a. Some birds can fly b. Elephants never forget

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1-CMakekup of the StudyCN 6

You hire and assistant to help you with the study of teenage employment.

Is the teen a boy or girl? Is the teen an honor student or not? Is the teen employed or not?

He focuses on a small group of teens who are all enrolled in the same school. He reports

Some of the honor-student boys are unemployed Some of the non-honor student girls are employed

Make a Venn diagram and put X’s in the appropriate places to indicate the regions that you can be sure have members.

6. Based on this report, do you know whether any of the school’s honor-student girls are unemployed, why or why not?

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1-CColor MonitorsCN 7

Color television and computer monitors make all the colors you see by combining pixels (short for picture elements) that display just three colors: red green, and blue. In pairs, these combinations of colors give the following results (with colors at equal strength) Yellow, purple, Cyan. White is made by combining all three colors, and black is made by using none of the colors.

7. Draw a Venn diagram to represent all this color information.

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1-C

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Blood Types

Venn Diagrams with Three SetsExample 8

1-CHomework 1C

DP of 1B CN 1-7 Quick Quiz p.45 1-10 p.46:1-12 1 web

88. State Politics 89. US Presidents 90. Web Venn Diagrams

1 world 91. Categorical Propositions 92. Venn Diagrams in Your Life 93. Quantitative Diagram

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