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The answer for: 1)Give me a group of girls whose height is > than 156 cm is E,F,G. 2) The answers for Piano and Guitar question is: n(U) =8, n(A)=3, n(B)=4 (A n B) = 1 ( A U B)= 6 (A U B)' = 2 Only Piano ( A - B)=2 Only guitar(B-A) =3 Sets [Algebra] in an easier and interesting way to learn! Specially suited for young children and for those who find Sets difficult to grasp. Content- Venn diagram, Set builder(Rule method), List method(Roster method), Universal set, Union of sets, Intersection of set
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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