Question:

In a city, $20$ percent of the population travels by car, $50$ percent by bus and $10$ percent travels by both car and bus. Then person travelling by car or bus is

Updated On: Jul 6, 2022

$80\%$
$40\%$
$60\%$
$70\%$

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The Correct Option is C

Solution and Explanation

Let population be

100

. Let

A

and

B

be the sets consisting of population which travels by car and by bus respectively.

n(A) = 20

n(B) = 50

and

n(B \cap A) = 10

n(A \cup B) = n(A) + n(B) - n(A \cap B)

= 20 + 50 - 10 = 60\%

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Notes on Sets

Concepts Used:

Sets

Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.

Example of set: Set of vowels A={a,e,i,o,u}

Representation of Sets

There are three basic notation or representation of sets are as follows:

Statement Form: The statement representation describes a statement to show what are the elements of a set.

For example, Set A is the list of the first five odd numbers.

Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.

For example represent the set of vowels in roster form.

A={a,e,i,o,u}

Set Builder Form:

The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
Sometimes a ":" is used in the place of the "|".

In a city, 202020 percent of the population travels by car, 505050 percent by bus and 101010 percent travels by both car and bus. Then person travelling by car or bus is