SETS [Algebra]

SETSSTD- IX

(Algebra)

By Natasha Pereira

The heights (in cm) of 8 girls in class X are as follows:

Girl A B C D E F G H

Height(in cm) 152 155 156 153 160 157 154 159

1)List the tall girls in the class (Different students will give different answers)

The heights (in cm) of 8 girls in class X are as follows:

Girl A B C D E F G H

Height (in cm) 152 155 156 153 160 157 154 159

2) Give me a group of girls whose height is greater than >156 cm. i) {A, B, C }ii) {C, E, F , H}iii) {E, F, H}

Now you are able to give a correct answer because it a well defined collection of objects.

What is a Set?-A set is a collection of well defined objects

Examples:

1) A set of colors in a rainbow 2) A set of days in a week

3) A set of vowels in the English alphabet

Methods of Writing Sets

1) Listing method (Roster form)

2) Rule method (Set builder form)

1) Listing method (Roster form)Its simple - Listing means to list out

Examples:

i) A is a set of vowels A = { a, e, i , o, u }

ii) B is a set of Prime numbers between 10 to 20 B = {11, 13, 17, 19}

iii) C is a set of first five cubes C = {1, 8, 27, 64, 125}

iv) D is a set of letters of the word DIVISION D = { D, I, V, S, O, N }

2) Rule method (Set builder form)As the word rule means- it follows a certain form of rule

Examples:

i) Consider the set A ={1, 4, 9, 16, 25}Rule method: A = {x|x=n² , n N, n=1,2,3,4,5} It is read as: x such that x=n² , n belongs to a Natural number

and n=1,2,3,4,5

ii) Consider the set B= {11, 13, 17, 19}Rule Method: B={x|x is a Prime number, 10 < x < 20}

iii) Consider the set C={−3, −2, −1, 0, 1, 2, 3}Rule method: C={x|x is an integer, −3 x 3 }

Illustration:

Listing method (Roster form)

Rule method (Set builder form)

A = { a, e, i, o, u } A = {x|x is a vowel in English alphabet}

B= { 11, 13, 17, 19} B = { x|x is a prime number, 10< x <20}

C= {−3,−2,−1, 0, 1 ,2,3} C={x|x is an integer, and −3 x 3 }

D= { 1, 4, 9, 16, 25 } D = {x|x =n² , and n= 1,2,3,4,5}

Look at the Venn diagram and answer:

Football Tennis

Both Games

No Games

Q) How many people are there in all?Ans: 13 People

Q) How many people play Football?Ans: 7 People

Q) How many people play only Football?Ans: 5 People

Look at the Venn diagram and answer:

Football Tennis

Both Games

No Games

Q) How many people play Tennis?Ans: 5 People

Q) How many people play only Tennis?Ans: 3 People

Look at the Venn diagram and answer:

Football Tennis

Both Games

No Games

Q) How many people play both the Games?Ans: 2 People

Q) How many people play neither of the Games?Ans: 3 People

Look at the Venn diagram and answer:

Football Tennis

Both Games

No Games (A B)

AB

(B−A)(A−B)

(A B)U

Look at the Venn diagram and answer:

Football Tennis

Both Games

No Games (A B)

AB

(B−A)(A−B)

(A B)U

Q) How many people are there in all?Ans: U=13 people

Q) How many people play Football?Ans: n(A)=7

Look at the Venn diagram and answer:

Football Tennis

Both Games

No Games (A B)

AB

(B−A)(A−B)

(A B)U

Q) How many people play both Games?Ans: (A B) = 2

Look at the Venn diagram and answer:

Football Tennis

Both Games

No Games (A B)

AB

(B−A)(A−B)

(A B) U

Q) How many people play Football? Ans: n(A)= 7 Q) How many people play only Football?Ans: n(A−B) = n(A) − n(A B) = 7 − 2 = 5

Look at the Venn diagram and answer:

Football Tennis

Both Games

No Games (A B)

AB

(B−A)(A−B)

(A B) U

Q) How many people play Tennis?Ans: n(B)= 5 Q) How many people play only Tennis?Ans: n(B−A) = n(B) − (A B) = 5 − 2 = 3

Look at the Venn diagram and answer:

Football Tennis

Both Games

No Games (A B)

AB

(B−A)(A−B)

(A B) U

Q) How many people play atleast one of the two Games?Ans: n(A B) = 10

Q) How many people play neither of the Games?Ans: n(A B) = 3

Assignment:

Piano GuitarA B

None

n (U) = *Only Piano (A−B) =(AB)= *Only Guitar(B−A) =(AB)=(AB)= n(A)= n(B) = *Use the formula (A−B) = n(A)− n(A B)

Assignment:

Piano GuitarA B

Both

None

n (U) =

Assignment:

Piano GuitarA B

None

n(A)=

Assignment:

Piano GuitarA B

None

n(B) =

Assignment:

Piano GuitarA B

None

(AB)=

Assignment:

Piano GuitarA B

None

(AB) =

Assignment:

Piano GuitarA B

None

(AB) =

Assignment:

Piano GuitarA B

None

*Only Piano (A−B) =Use the formula (A−B) = n(A)− n(A B)

Assignment:

Piano GuitarA B

None

People playing only Guitar(B−A) = n(B)− n(A B)

THE ENDThank you

Happy studying