(ii) Find the number of students who liked both the drinks.
(iii) Find the number of students who didn't like tea only.
Answer: (i), (ii) 310 students, (iii) 140 students
Solution:
Let the set of total students be U.
Let T and C denote the sets of students who liked tea and coffee, respectively.
Given,
$n(U) = 750$
$n(T) = 520$
$n(C) = 450$
$n ( \overline{T \cup C}) = 90$
To find:
(i) $n(T \cap C) = ?$
(ii) $n_o(C) = ?$
We know,
$n(U) = n(T) + n(C) - n(T \cap C) + n(\overline{T \cup C})$
$or, 750 = 520 + 450 - n(T \cap C) + 90$
$or, 750 = 970 + 90 - n(T \cap C)$
$or, n(T \cap C) = 1060 - 750$
$\therefore n(T \cap C) = 310$
And,
$n_o(C) = n(C) - n(T \cap C)$
$or, n_o(C)= 450 -310$
$\therefore n_o(C) = 140$
Hence,
The required number of students who liked both the drinks were 310 students and who didn't like tea only were 140 students.
Explanation to answer (iii)
In question (iii), it has asked those who didn't like tea only. It certainly wants to say that the students like at least one drink but they do not like tea. Which ultimately means the students like coffee only. Thus, we found the number of students who liked coffee only.
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