Finite and Infinite Sets, Null set

Finite and Infinite Sets, Null setFinite Set is the set there are the elements equal

Integer numbers or zero.

If A repersents the set , then repersents the numbersof elements in the set,we write n(A)

In an finite set all the members of the set can be listed.

or #(A)

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A = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Example n(A)

= 9

We say “ the set A is finite Set”B = {1, 2, 1, 2, 12}

n(B) = 3

We say “ the set B is finite Set”C = {x | x is odd numbers between 10 and 26}

C = {11, 13, 15, 17, 19, 21, 23, 25}

n(C) = 8 We say “ the set C is

finite Set”

D = {x | x is motor-cycles in Phitsanulok

Pittayakom School}

We say “ the set D is finite Set”E = {x | x is a letter of the English alphabet}n(E) = 26

We say “ the set E is finite Set”F = {M, A, G, A, T, E}n(F) = 5

We say “ the set F is finite Set”

Infinite Set is the set A that we can continue writing down the elements of A indefintely, i,e., A has anInfinite numbers of elements.Exa

mpleN = {x | x is natural numbers}

Since, the elements of N has an infinte numbers. We say “ the set N is Infinite Set”

E = {x | x is even numbers}

Since, the elements of E has an infinte numbers. We say “ the set E is Infinite Set”F = {x | x is fractions}Since, the elements of F has an infinte numbers. We say “ the set F is Infinite Set”G = {x | x is squares}Since, the elements of G has an infinte numbers. We say “ the set G is Infinite Set”

P = {x I| x < -4}Since, the elements of P has an infinte numbers. We say “ the set P is Infinite Set”Q = {xR | o < x < 2}Since, the elements of Q has an infinte numbers. We say “ the set Q is Infinite Set”R = {xI | x ห�รืด$วย 5 ลงตว}Since, the elements of R has an infinte numbers. We say “ the set R is Infinite Set”

The empty set or the null setA set which contains non elements is called an empty set or a null set. It is denoted by { } or .

ExampleA = {x R | x2 = -9}

We say “ the set A is null Set” Such that, A =

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B = {x | xN , x + 5 = 3} We say “ the set B is null Set” Such that, B =

C = {xN | 1 < x < 2} We say “ the set C is null Set” Such that, C =

D = {xI | x2 = 3} We say “ the set D is null Set” Such that, D =

Universe SetUniverse SetThe set which contains all the orther sets in a discussionIs called the universal set.

This is usually by the symbol U.ExampleU = The set of students in Phitsanulok Pittayakom School.U = The set of positive integers.

Equal Sets and Equivalent Sets

Equal Sets and Equivalent Sets

Definition Two set A and B equal , if and only if they have exactly the same elements.It is written A = B

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Equal SetsEqual Sets

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Equivalent SetsEquivalent Sets

Definition Two set A and B Equivalent , if and only if numbers of elements two set are equal.It is written A B

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Example 10

Let A = {2, 3, 5, 7} B = { x I+| x is prime numbers , x < 10}

B = { 2, 3, 5, 7}

Hence, A = B and A B Example 11

Let E = {2, 4, 6, 8} F = { x I | x is even numbers , x < 10}

F = { . . . , -4, -2, 0, 2, 4, 6, 8}

Hence, E = F and E F

Example 12

Let T = {1, 2, 3, 4} S = { x I| 0 < x 4}

s = { 1, 2, 3, 4}

Hence, T = S and T S Example 13

Let D = {1, {2}} F = {{1}, {2}}

Hence, D = F but D F

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Example 14 Consider the following sets, two sets are aqual.A = {x | เป็+นพยญชินะในคื��ว�� ส(ดสวย“ ”}

B = {x | เป็+นพยญชินะในคื��ว�� ส�ยสว�ท่“ ”}C = {x | เป็+นพยญชินะในคื��ว�� วยสดสวย“ ”}D = {x | เป็+นพยญชินะในคื��ว�� วดสวย“ ”}

A = {ส, ด, ว, ย} B = {ส, ย, ว, ท่} C = {ว, ส, ด, ย} D = {ว, ด, ส, ย}

Hence, A = C = D

Example 15 Consider the following sets, two sets are aqual.E = {0, 1, 2, 3, 4}

F = {x I | x3 – 4x2 + 3x = 0}G = {xI | -1 < x 4}H = {xR| -1< x 4}

F = {0, 1, 3} G = {0, 1, 2, 3, 4} Hence, E = G