Question:
In a class containing 120 students, 65 students drink tea and 84 students drink coffee. It x students drink both tea and coffee, what is the value of x ?
In a class containing 120 students, 65 students drink tea and 84 students drink coffee. It x students drink both tea and coffee, what is the value of x ?
Updated On: Jul 6, 2022
- 39
- 65
- $29 \le x \le 65$
- $29 \le x \le 84$
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The Correct Option is C
Solution and Explanation
Let T denote the set of students who drink Tea and C denote the set of students who drink coffee. As given:
n (T) = 65, n (C) = 84,
Let x denote number of students who take tea and coffee both.
n(T $\cup$ C) = 120 and n(T $\cap$ C) = x
n(T $\cup$ C) = n(T) + n(C) - n(T $\cap$ C)
$ \Rightarrow \, 120 \ge 65 + 84 - x $
$x \ge 149 - 120 \ge 29$ and $x \le n (T)$
$\Rightarrow \, x \le 65 \therefore \, 29 \le x \le 65$
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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:
- 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 "|".