Problems Involving Sets - Questions - Class Mathematics School Portal

Problems Involving Sets - Questions

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Question 1

30041

In a class of 30 students it is known that 20 had at least one brother and 14 had at least one sister and 4 had neither a brother or a sister. How many have both?

Answer

$8$

Worked Solution

$$
\begin{aligned}
&\text{From the venn diagram}\\
&\begin{aligned}
20-x+x+14-x+4&=30 \\
38-x&=30 \\
\therefore x&=8
\end{aligned}\\
&\therefore\ 8\ \text{had both.}
\end{aligned}$$

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