2. Thinking Critically
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3. Sets and Venn Diagrams Unit 1C
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4. 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.
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5. 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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6. Venn Diagram for Categorical Propositions
The set whales is a subset of the set mammals.
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7. Venn Diagram for Categorical Propositions
other animals
The set of fish is disjoint from the set mammals.
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8. Venn Diagram for Categorical Propositions
men who are not doctors
male doctors
female doctors
women who are not doctors
The sets of doctors and women are overlapping.
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9. Real Number Venn Diagram
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10. Categorical Propositions
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.
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11. Constructing a Venn Diagram
Statement: “Some dogs can swim.”
Rephrase to: “Some dogs are animals that can swim.”
Construct the Venn diagram:
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12. Venn Diagrams with Three Sets
Blood Types
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