finite and infinite sets, null set

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