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 }
Mathematics for Junior High School Year 7 /219
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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.
Mathematics for Junior High School Year 7 /221
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