Lesson
Notes
Sets and Venn Diagrams
Fall 2014 - Math 1030
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Checklist
Notes
Use set notation.
Construct Venn diagrams.
Use diagrams for categorical propositions.
Negate categorical propositions.
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Assignment
Notes
Assignment:
1. p 45 - 46 Quick Quiz
2. p 46 - 49 Excersizes 29, 37, 43, 45, 57, 59, 61, 67, 73,
78, 83
3. Begin reading 1D
4. Quiz: January 16 (Section 1C and 1D)
Each section’s quick quiz is very helpful!
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Key Words
Notes
Set - A collection of objects; these objects are named
members.
Venn diagram - Visual way of describing relationships
between sets.
Subset - A collection of some members of a set.
Disjoint sets - Two sets with no common members.
Overlapping sets - Members in common of two sets.
Categorical proposition - Statements making a claim
about a set.
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Sets
Notes
A set is a collection of objects. Set notation is a common
form of describing a set:
The set of all lower-case alphabet letters:
{a, b, c, . . . , x, y , z}
The set of all upper-case alphabet letters:
{A, B, C , . . . , X , Y , Z }
These examples used ellipses (. . .) to indicate both a
pattern and the members not listed.
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Venn Diagrams
Notes
Venn diagrams are visual ways to describe the relationship
between two sets.
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Venn Diagrams - Subsets
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Notes
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Venn Diagrams - Overlapping sets
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Categorical Propositions
Notes
A categorical proposition is a statement making a claim
about a set.
”All whales are mammals.”
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Categorical Propositions
Notes
Categorical propositons come in four standard forms.
Here S is the subject set and P is the predicate set.
Form
All S are P
No S are P
Some S are P
Some S are not P
Example
All whales are mammals.
No fish are mammals.
Some doctors are women.
Some teachers are not men.
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Categorical Propositions
Notes
Rephrasing statements such as, ”all diamonds are
valuable,” or, ”some birds can fly,” requires us to create a
predicate set.
This first statement may read ”all diamonds are things of
value.” The subject set S = diamonds, and predicate set
P = things that are valuable.
The next may read ”some birds are animals that can fly.”
S = birds and P = animals that can fly.
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Notes