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Learning Objectives : upon completion, you should be able to
perform the following operations:
Union
Intersection
Complement
Difference
Cross product
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Uses a closed region in the plane to
represent sets.
A B C
U
Universal set
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A B
U
A B
A
B
A = B
U
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The union of two sets A and B, denoted by , is the set
consisting of all elements belonging to either sets A or set B.
or A B x x A x B
A B
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U
A B
A B
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If
A = {dog, cat, rat, pig, cow, fly} and
B = {ant, bee}
then,
dog,cat,rat,pig,cow,fly,ant,bee .A B
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| is a positive odd integer less than 10A x x
1,2,3,4,5B
Then, 1,3,5,7,9,2,4 .A B
Let
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The intersection of two sets A and B,
denoted by , is the set of all
elements common to both set A and set
B.
and A B x x A x B
A B
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A B
A B
U
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If
A = {2, 4, 6, 8, } and
B = {5, 10, 15, }
Then,
is a positive multiple of 10 .A B x x
10,20,30,40,
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Let
| is a positive odd integer less than 10A x x
1,2,3,4,5B
Then, 1,3,5 .A B
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If A B = , we say A and B are disjoint.
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A B
U
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Let
| is a negative numberA x x
is a positive numberB x x
Then, .A B
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The complement of a set A, denoted by
, is a the set of all elements of
the Universal set which are not
elements A.
but CA x x U x A
or 'CA A
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AC
A
U
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Let
1, 2,0,1,2,3,4,
1,2,3,4,
U
N
Then, 1, 2,0 .cN
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The difference between sets A and B,
denoted by A-B, is the set of elements of
A which are not elements of B.
but A B x x A x B
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AB
A B
U
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BA
B
U
A
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Let
1,3,5,7,9
4,5,6,3
A
B
Then,
1,7,9
4,6 .
A B
B A
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Let
0,1,2,3,4,
1,2,3,4,
W
N
Then,
W- 0
.
N
N W
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A BThe cross product of two sets A and B,
denoted by , is the set of all
ordered pairs where ,x y and .x A y B
, and A B x y x A x B
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Let A = {1, 2, 3} and B = {a, b}.
Then,
A x B = {(1,a), (1,b), (2,a), (2,b), (3,a), (3,b)}.
B x A={(a,1), (b,1), (a,2), (b,2), (a,3), (b,3)}.
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A
1
2
3
B
a
b
A x B
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In this section, we learned how to perform
the following set operations:
Union
Intersection
Complement
Difference
Cross product
Set Operations
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Prepare for a GRADED
EXERCISE on Unit 1: Set,
Set Relations and Set
Operations.
