# 2.1 Basic Set Concepts by pptfiles

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```									2.1 Basic Set Concepts
Set
2 : a number of things of the same kind that belong or are
used together [an electric train set]
21 : a collection of elements and especially mathematical
ones (as numbers or points)- called also class (MWD)

The objects in a set are called elements or members.

A set must be well defined. The elements must be clearly
determined. From the definition of the set we must be
able to determine if an element is or is not a member of
the set.
The days of the week form a set. Tuesday is an element
of the set of days of the week.
Using the roster method, we list the elements of the set.
W = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday

Will the great presidents of the United States form a set?
Is the group well defined?
Express the set of months of the year using the roster method.

Write a word description of the set L={a, b, c, d, e}

The set of the first five letters of the alphabet.
Set Builder Notation

J is the set of all x such that x is a month with a name that
starts with J

Express the set W={2, 4, 6, 8} using set builder notation.

Express the set E={x | x is month that begins with the letter E}
using the roster method.
There are no elements in set E. We express this as { } or Ø.
We call a set with no elements an empty set or a null set.
p is an element of the set containing n, o, p, q, r, s.

k is not an element of the set containing n, o, p, q, r, s.
Which symbol will make the statement true?

Natural or Counting Numbers ¥ = { 1, 2, 3, 4, 5, 6, …}
Set B is the set of Natural numbers less than 4.
Express B using the roster method.

Set R is the set of Natural numbers between 7 and 11.
Express R using the roster method.

Set L is the set of Natural numbers between 25 and 412.
Express L using the roster method.
Cardinal Number

The cardinal number of a set is the number of elements in
the set.
If A={3, 7, 8, d, e}, then n(A)=5
What is the cardinality of M, if M={6, 7, 8, 9}?
n(M)=4

What is the cardinality of P, if P={1, 2, 3, …16, 17}?

n(P)=17

What is the cardinality of Z, if Z={4, 5, 6, …23, 24}?

n(Z)=21
What is the cardinality of Q, if Q={2, 4, 6, … 32, 34}?
n(Q)=17

What is the cardinality of A, if A={1, 3, 5, …45, 47}?

n(A)=24

What is the cardinality of Y, if Y={7, 10, 13, …94, 97}?

n(Y)=31
Sets are equivalent if they have the same cardinality.

{ Ω, π, µ, ∂} is equivalent to { 5, 7, 13, f }

Is {a, b, d, e, a} equivalent to {3, 4, 5, 6} ?

They both have a cardinality of 4. They are equivalent sets.

Is {1, 3, 5, 3, 5} equivalent to {A, B, A, 6} ?

They both have a cardinality of 3. They are equivalent sets.
Set A is a finite set if n(A)=0 or n(A) is a natural number.

A set that is not finite is called an infinite set.

{1, 2, 4, 8, 16, 32, … } is an infinite set.

Sets are said to be equal if they contain exactly the same
elements.

{Ralph, Alice, Ed, Trixie}={Alice, Trixie, Ed, Ralph}

{x|x is a natural number less than 100}={1, 2, 3, … 98, 99}

{ 2, 3, 4, 5, 2, 3 } = { 5, 3, 2, 4 }

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