Question:

In a group of 500 students, there are 475 students who can speak Hindi and 200 can speak Bengali. What is the number of students who can speak Hindi only ?

Updated On: Sep 17, 2024
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The Correct Option is B

Solution and Explanation

Total number of students = 500 Let H be the set showing number of students who can speak Hindi = 475 and B be the set showing number of students who can speak Bengali = 200 So, n (H) = 475 and n (B) = 200 and given that n (B $\cup$ H) = 500 we have n (B $\cup$ H) = n (B) + n (H) - n (B $\cap$ H) $\Rightarrow$ 500 = 200 + 475 - n (B $\cap$ H) so, n (B $\cup$ H) = 175 Hence, persons who speak Hindi only = n (H) - n $\cap$ H) = 475 - 175 = 300
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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: 

  1. The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
  2. The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
  3. 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.
  4. Sometimes a ":" is used in the place of the "|".