First slide

Operations on Sets

Question

Out of 64 students, the number of students taking Mathematics is 45 and number of students taking both Mathematics and Biology is 10. Then, the number of students taking only Biology is

Easy

Solution

Let M and B denote the number of students taking Mathematics and Biology.
Then,
$\begin{matrix} n (M) = 45, n (M \cap B) = 10, n (M \cup B) = 64 \\ ∴ n (B) = n (M \cup B) - n (M) + n (M \cap B) \\ = 64 - 45 + 10 = 29 \\ \Rightarrow n (only B) = n (B) - n (M \cap B) = 29 - 10 = 19 \end{matrix}$

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