Sets and Venn Diagrams

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Sets and Venn Diagrams
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Sets A B C

A SET is a collection of objects. They can be
numbers, words or things. SETS are named using a
capital letter. Objects are listed inside
brackets.
A 2, 3, 5, 7, 11, 13
B square, rectangle, trapezoid, rhombus,
parallelogram
C desk, chair, students, whiteboard, computer,
teacher
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Element (of a Set) ? ?
An ELEMENT of a set is a member of the set. The
symbol ? means is a member of and the symbol
? means is not a member of
7 ? A
A 2, 3, 5, 7, 11, 13
10 ? A
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Subset (of a Set) ? ?
A SUBSET of a set is a set that contains some or
all of the elements of the set, but no other
elements. The symbol ? means is a subset of
and the symbol ? means is not a subset of.
B ? A
A 2, 3, 5, 7, 11, 13 B 3, 5, 7 C 1, 2,
3, 4
C ? A
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Subset (of a Set) ? ?
A
B
B ? A
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Union (of 2 Sets) ?
A UNION of 2 sets is a set that contains all of
the elements of both sets. Common elements are
listed only once. The symbol ? means union
of.
A 3, 5, 7, 9 B 1, 2, 3, 4, 5, 6
A ? B
1, 2, 3, 4, 5, 6, 7, 9
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Union (of 2 Sets) ?
B
A
x, 3
A 1, 2, 3, 4, x B 3, w, x, y, z
A ? B 1, 2, 3, 4, w, x, y, z
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Intersection (of 2 Sets) ?
An INTERSECTION of 2 sets is a set that contains
only those elements that are in both sets. The
symbol ? means intersection of.
A 3, 5, 7, 9 B 1, 2, 3, 4, 5, 6
A ? B 3, 5
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Intersection (of 2 Sets) ?
B
A
x, 3
A 1, 2, 3, 4, x B 3, w, x, y, z
A ? B x, 3
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Empty or Null Set ?
An EMPTY OR NULL SET is a set that contains no
elements. The symbols or ? stand for an
empty or null set.
A ? B
A 3, 5, 7, 9 B 2, 4, 6, 8
or
A ? B ?
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Empty or Null Set ?
B
A
A 1, 2, 3, 4 B w, x, y, z
A ? B or ?
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Complement A
The COMPLEMENT of set A is all elements of the
universal set, U, not in set A. The Universal
set will be defined for the situation. The
complement is denoted with a .
U Odd numbers lt 10
A 1, 5, 9
A 3, 7
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Complement A
U Factors of 24
A
1, 2, 3, 4, 6
A 8, 12, 24
A 1, 2, 3, 4, 6
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Additional Terms
Types of Set Notation

• Description Notation (describes the set)

I the set of integers A the set of odd
numbers less than 20

• Roster Notation (lists the elements of the set)

I , -3, -2, -1, 0, 1, 2, 3, A 1, 3, 5,
7, 9, 11, 13, 15, 17, 19

• Set Builder Notation (gives the property that
  defines each element)

I xx is an integer A xx is an odd whole
number less than 20
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Additional Terms

• Infinite Set a set whose elements cannot
  becounted or listed

I , -3, -2, -1, 0, 1, 2, 3,

• Finite Set all elements can be counted orlisted

A 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
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Additional Terms

• Equal Sets two sets that contain the
  sameelements but not necessarily in the same
  order

A c, 0, 1, d B d, 1, 0, c

• Equivalent Sets two sets that contain thesame
  number of elements

A 1, 2, 3 B 4, 5, 6