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Q.
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 ?
Sets
Solution:
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 $x \le n (T)$
$\Rightarrow \, x \le 65 \therefore \, 29 \le x \le 65$