Semi Detailed Lesson Plan In Mathematics Pdf

S E T S

I. SETS AND MEMBERS OF SET

Example: A = { 1, 2, 3, 4, 5, 6} The members of set A are 1, 2, 3, 4, 5, and 6, there for we can write: 1

∈

A 7

∉

A 2

∈

A 9

∉

A 3

∈

A and 12

∉

A 4

∈

A 16

∉

A 5

∈

A 20

∉

A 6

∈

A 35

∉

∈

means

element

and

∉

means

not element

II. EXPRESSING SETS

Three ways to expressing sets, there are: 1. By expressing sets in words Example: B = { prime less than ten } 2. By roster way Example: C = { 2, 3, 5, 7 } 3. By forming notation Example: D = { x



x < 10, x

∈

prime }

III. CARDINALITY OF SETS

Look at the following sets: E = { a, b, c, d, e } F = { 1, 3, 5, 7, … , 15 } G = { 3, 6, 9, 12, … } H = { …, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 } - Set E has 5 elements, we can write n (E) = 5 - Set F has 8 elements, we can write n (F) = 8 For sets E and F we can count the number of the elements of set, thus sets E and F are called

countable

sets

finite sets

. Now for sets G and H, we are not able to count the number of elements of both sets. These kinds of sets are called

uncountable sets

infinite sets

W O R K S H E E T

1. Look at the following sets: K = { 5, 10, 15, 20, 25, 30 } L = { 1, 2, 3, 4, 6, 8, 12, 24 } M = { 4, 8, 12, … , 48 } Answer the questions below by fill in the blank. a. The elements of K are …, …, …, …, …, and …. Fill the blank by '

∈

' or '

∉

' Thus 5 … K 20 … K 25 … K 6 … K 14 … K 50 … K b. The elements of L are …, …, …, …, …, …, …, and …. Fill the blank by '

∈

' or '

∉

' Thus 2 … L 4 … L 12 … L 21 … L 28 … L 32 … L c. The elements of M are …, …, …, …, …, …, …, …, …, …, …, and …. Fill the blank by '

∈

' or '

∉

' Thus 16 … M 36 … M 40 … M 52 … M 44 … M 72 … M 2. Expressing the following sets using three ways. a. The set of the first five natural numbers. Answer: - By expressing sets in word: { the ………………………………… ………} - By roster way: { …, …, …, …, … } - Forming notation: { x



………………………………… …..} b. The set of the factor of 18 Answer: - By expressing sets in word: { the ………………………………… ………} - By roster way: { …, …, …, …, …, … } - Forming notation: { x



………………………………… …..} c. The set of the letter on word " MATEMATIKA" Answer: - By expressing sets in word: { the ………………………………… ………} - By roster way: { …, …, …, …, …, … }

- Forming notation: { x



………………………………… …..} 3. Expressing the following sets by the others ways. a. N = { x



2 < x < 7 , x natural numbers} Expressing by word : { ……………………between ………………… } b. P = { the odd number between 6 and 36 } Expressing by roster way: { …, …, …, …, …, …, …, …, …, …, …, …, …, …, … } c. Q = { 4, 6, 8, 10, 12, 14, 16, 18 } Expressing by forming notation: { x



……………………………………..} 4. Look at the following sets. R = { 1, 2, 3, …, 10 } S = { 10, 20, 30, 40, … } T = { the factor of 56 } V = { x



3 < x < 18 , x even number} W = { the odd prime numbers } a. The countable sets are …, …, and …. b. The uncountable sets are … and …. c. Counting every sets and thus: n (R) = …. n (S) = …. n (T) = …. n (V) = …. n (W) = ….

IV. VENN DIAGRAM A. UNIVERSAL SETS ( U )

Example: Given A = { 2, 3, 5, 7, 11 } The possible universal sets of A are:

U = { 1, 2, 3, …, 15 } 2.U = { the first ten prime number } 3.U = { 1, 2, 3, … , 20 } 4.U = { natural numbers } 5.U = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41 } 6.etc.

B. VENN DIAGRAM

Examples: 1. Given U = { 1, 2, 3, 4, 5, 6, 7, 8 }, and A = { 2, 3, 5, 7 } The Venn diagram of those sets is: