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Examples 3 In a survey it was found that 8.%people like oranges ,85% like mangoes and 75% like both But 45 people like n...
12/05/2020

Examples 3

In a survey it was found that 8.%people like oranges ,85% like mangoes and 75% like both But 45 people like none of themDrawing Venn –diagram , find the number of the people whowere in the survey.

Soln:
Let O and M be the number of people who like oranges and mangoes respectively.

n (U) =n(OUM) + n(OUM)c

100%=n (O) + n (M) - n(O∩M) + n(OUM)c

100% =80% + 85% - 75% + n(OUM)c

n(OUM)c= 10%

According to the question,

10%of total number(say x)= 45

Or, x=4500/10 = 450

Examples 2In the certain examination, 50% students passed in account, 30% passed in English, 30% failed in both and 25 s...
12/05/2020

Examples 2

In the certain examination, 50% students passed in account, 30% passed in English, 30% failed in both and 25 student passes in both subjects. By drawing Venn – diagram, find the number of the students who passes in account only.
Let total number be x A and E denotes the students who study account and English respectively

n(A) =50%
n(E) = 30%
n( A U E)c = 30%
n( A U E) = 25

We have
n(U)= n(A)+ n(E)+n(AUE)c
- n( A ∩E)

100%= 50 % + 30% + 30 % - n( A ∩E)

n( A ∩E) = 10%
According to the question,

10% of x = 25

x= 250

The number of the students who passed in accounts only = 40% of the 250 = 100

Examples1In a group of 200 students who like game, 120 like cricket game an 105 like football game. By drawing Venn diag...
12/05/2020

Examples1

In a group of 200 students who like game, 120 like cricket game an 105 like football game. By drawing Venn diagram find

i. how many students like both the games ?
ii. How many students like only cricket?

Soln

n(U) = 200
C and F denote the students who study Cricket and football respectively.

n(C) =120

n(F) = 105

n( C ∩ F)=?

We have

n(CUF)=n(C) + n(F) -n(C∩ F)

200=120 + 105 -n(C∩ F)

n(C∩ F)= 25

n0(C) = n(C)-n( C ∩ F)= 120 – 25 = 95

For exampleU = {1, 2, 3, 4, …………..50}A = {even integers from 1 to 50}B= {odd numbers from 1 to 50}Here, A and B are the ...
12/05/2020

For example

U = {1, 2, 3, 4, …………..50}
A = {even integers from 1 to 50}
B= {odd numbers from 1 to 50}

Here, A and B are the subsets of U



Overlapping sets
Two sets are said to be overlapped if they have same element in common.
A∩ B = {6}
A and B are overlapping sets.



Disjoint sets
Two sets are said to be disjoint sets if there is no element in common.

Cardinality of the sets
The number of the elements in the given sets is known as cardinality of sets.

A = {1, 2, 5,}
B = {5, 3, 4}
AUB = {1, 2, 3, 4, 5}

n(A) =3
n(B) = 3
n(AUB) = 5

Cardinality of the three sets
n(AUBUC) =n(A) + n(B) + n(C) - n(A∩ B) -- n(B∩ C) - n(C∩ A) +n(A∩ B∩ C)

SETSSets-: In mathematics set is defined as the collection of well defined object which can be separated distinctly.For ...
12/05/2020

SETS

Sets-: In mathematics set is defined as the collection of well defined object which can be separated distinctly.

For instance,
S = {2, 4, 6, 8} is collection of the even integers.

A set can be explained in different ways:

i. Listing method: A = {a, b, c, .z}

ii. Descriptive method: N = {the natural numbersfrom 1 to 50}

iii. Set builder method: A – B= A -(A∩ B )

iv. Venn – diagram

Universal sets-:A universal set is the collection of all objects in a particular context or theory. All other sets in that framework constitute subsets of the universal set, which is denoted as letter U. The objects themselves are known as elements or members of U.

Subsets-:The set made by elements of the universal sets is called subsets of the universal sets

For example

U = {1, 2, 3, 4, …………..50}
A = {even integers from 1 to 50}
B= {odd numbers from 1 to 50}

Here, A and B are the subsets of U

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