2.1 Basic Set Concepts by pptfiles

VIEWS: 0 PAGES: 13

									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 }

								
To top