BUKSIS-6.2 BARU

8/14/2019 BUKSIS-6.2 BARU

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at are you going tolearn?

Methods of Expressing Sets

You have learned that the set of football players can

be stated in the form of: To m ent ion va rious

ways of expressingsets

To c ha nge the set

exp ression from one

way to a no the r

Key Words:

{Football players}

In mathematics a set can be defined in several

methods. For example, we have the set of prime

numbers less than10. This set can be written as:

{Prime numbers less than 10}.

ways of expressing

sets The method above is called expressing sets by

description.roster

set b ui lde r nota tion If we have P = {Prime numbers less than 10}, thenwe can write the elements of P, namely 2, 3, 5, 7.

If all members of P are written consecutively

enclosed by a pair of curly brackets, and each two

members are separated by comma (,), then we get:

P = {2, 3, 5, 7}

This method of expressing the set P by listing all of

its elements is called the roster method.

So:

P = the set of prime numbers less than 10

can be written as follows:

P = {2, 3, 5, 7}

Some examples of sets expressed by roster are:

1. K = {1, 3, 5, 7, 9}

2. L = {January, June, July}

3. M= {1, 2, 3, 4, . . . , 100}4. N= {7, 14, 21, 28, . . .}

Mathematics for Junior High School Year 7 /217


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Consider set P = {2, 3, 5, 7}. The elements of set P satisfy a certain

condition, that is each element of P is a prime number less than 10.Therefore, set P can also be expressed as follows:P = { x| x prime number less than 10 } or

P = { x| x < 10, x prime }

Remarks:

1. The element condition is written after the symbol x|

2. The expression reads P is the set having elements of all x

such that xis prime numbers less than 10.The way above is called the set-builder notation.

Some other examples of expressing sets using set-builder

notation are:

a. K= { 0, 1, 2, 3, . . . , 10 } can be written as:

K= { n | n is whole number not greater than 10}

or

K= { n | n is whole number less than 11 }

orK= { n | n < 10, nW}; W= the set of whole numbers or

K= { n | n < 11, nW}; W= the set of whole numbers

b. M= { 1, 2, 3, . . . , 99 } can be written as:

M= { a | a is natural number less than 100}

or

M= { a | a < 100, aA }; A = the set of natural numbers

c. N= { 7, 14, 21, 28, . . . } can be written as:

N= { m | is natural number multiple of 7 }

From the above explanation, you have learned how to express

sets in three methods. You remember those methods, dont you?

Explain the three methods.

/ Students Book - Sets218


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Acquiring the Sets of Numbers

At the elementary school you already learned several types of

numbers. From certain types of numbers a set can be formed,

resulting in several kinds of sets of numbers, such as:

1. C= Set of whole numbers, or

Remarks

* The prime

number is anatural numberhaving exactlytwo factors,namely oneand thenumber itself.

The compositenumber is anatural numberhaving more

than twofactors.

C= { 0, 1, 2, 3, . . . }

2. A = Set of natural numbers, or

A = { 1, 2, 3, 4, . . . }

3. G = Set of even whole numbers, or

G = { 0, 2, 4, 6, . . . }

4. J= Set of odd whole numbers, or

J= { 1, 3, 5, 7, . . . }

5. K= Set of square numbers, or

K= { 1, 4, 9, 25, . . . }

6. T= Set of cubic numbers, or

T= { 1, 8, 27, 64, . . . }

7. P = Set of prime numbers, or

P = { 2, 3, 5, 7, . . . }

8. K= Set of composite numbers, or

K= { 4, 6, 8, 9, . . . }

1. Express the following sets with set-builder

notation.a. K = set of natural numbers between 2 and 7b. L = { 10, 11, 12, 13, . . . }c. M= { 2 }

Solution:

a. K= { x | 2 < x < 7, x is a natural number }

b. L = { n | n > 10 , n is a whole number }

c. M= { x | x is an even prime number }



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2. Express the following sets by listing their elements.

a. N= { x | x is prime number greater than 10}

b. O = set of square numbers greater than 15

c. P = { n | 1 < n < 5, n is a natural number}

Solution:a. N= { 11, 13, 17, 19, . . . }b. O = { 16, 25, 36, 49, . . . }c. P = { 1, 2, 3, 4, 5 }

/ Students Book - Sets220


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1. Express the following sets by listing their elements.

a. A = set of even whole numbers between 20 and 30.

b. B = set of the first six natural numbers.

c. C = set of factors of 24.

d.D = set of the first five squared numbers.

e. E = set of the first seven even whole numbers.

f. F = set of multiple of 5 between 1 and 100.

g. G = set of letters forming the word mathematics.

h. H = set of multiple of 3 of natural numbers.

i. I = set of the first eight composite numbers.

j. J = set of prime numbers between 10 and 40.

2. Express the following sets by description.

a. A = { 6, 12, 18, 24, . . . }

b. B = { 23, 29, 31, 37 }

c. C = { 3, 5, 7, 9, 11 }

d.D = { 0, 2, 4, . . . 16 }

e. E = { 1, 4, 9, 16, 25 }

f. F = { 4, 6, 8, 9, 10, 12, 14, 15, 16, 18 }

g. G = { a, b, c, d, e, f, g, h }

h. H = { 4, 8, 12, 16, 20 }

i. I = { 5, 10, 15, 20, . . . }

j. J = { 1, 8, 27, 64, . . . }

3. Express the following sets with set-builder notations.a. A = { 12, 13, 14, 15, . . . , 25 }

b. B = { 11, 13, 17, 19, . . . }

c. C= set of even whole numbers not greater than 50.

d.D = set of odd numbers between 10 and 20.

e. E = {4, 6, 8, 10, 12, 14 }

f. F= {a, i, u, e, o }

g. G = set of the first four odd whole numbers.

h. H= {0, 1, 4, 9, 16, 25 }i. I = set of the first eight prime numbers.

j. J = set of multiple of 7 of natural numbers.



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