2'1 Basic Set Concepts

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2.1 Basic Set Concepts
SETS A collection of objects by some
classification or characteristics, known as
elements or members.
There are THREE ways of writing sets
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I. Roster Method
W 2, 4, 6, 8, 10
Name of the set is always a Capital Letter!!!!
NEVER use ( ), or in place of !!!
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II. Word Description
W is the set of N that are even and less than 12
N is always used to represent the counting or
natural numbers
Always be clear and concise!!!
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III. Set Builder Notation
such that
W x x is the set of even numbers less
than 12
is
the set of all
The set W
Combo of I and II !!!
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Roster Method
J 2, 3, 5, 7, 11, 13
Word Description
J is the set of prime numbers less than 17.
Set Builder Notation
J x x is a prime number less than
17.
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Roster Method
B 1, 4, 9, 16, 25
Word Description
B is the set of numbers that are perfect squares
less than 36.
Set Builder Notation
B x x is a number that is a perfect square
less than 36.
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Roster Method
H or H Ø
Word Description
H is the set of all months that start with X.
Set Builder Notation
H x x is month that starts with X.
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Pick one number in this set.
Ellipsis
1, 2, 3, 4, , 100
7 1, 2, 3, 4, , 100
Is an element of
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Pick one number NOT in this set.
Ellipsis
1, 2, 3, 4, , 100
111 1, 2, 3, 4, , 100
Is not an element of
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TRUE OR FALSE
h a, b, c, d, z
TRUE
6 2, 4, 6
FALSE
9 x x is an even number
T
True
x x N
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Write the following in Roster Method.
H x x N and x is odd.
H 1, 3, 5, 7,
R is the set of all counting numbers less than or
equal to six.
R 1, 2, 3, 4, 5
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Write the following in Roster Method.
W x x N and x is between 4 and 5.
H or H Ø
Q x x 5 7
Q 2
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The cardinal number or cardinality.
Cardinal Number Is the number of elements
in a set.
B a, e, i, o, u
n (B) 5 or the cardinality of B is 5.
The number of distinct elements in B
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Find the cardinal number of the following sets.
S 2, 4, 6, 8, , 50
n (S) 25
T Monday, Tuesday
n (T) 2
M
n (M) 0
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EQUAL vs EQUIVALENT
EQUAL Sets The sets being compared have exactly
the same elements regardless of order or possible
repetition. A B
EQUIVALENT Sets The sets being compared have the
same cardinal number
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EQUAL or EQUIVALENT ?
A 2, 4, 8, 10, 2 B 10, 8, 4, 2
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EQUAL or EQUIVALENT ?
A Monday, Tuesday, Friday B Red, Blue,
Yellow
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EQUAL or EQUIVALENT ?
A 1, 1, 8, 8, 13 B 1, 8, 13
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EQUAL or EQUIVALENT ?
A 1, 2, 3, , 50 B x x is a state in
the United States
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HomeworkPg 473 84 Multiples of 3