Question

In a group of 30 people, 12 have sisters and 15 have a brother. How many people have both a sister and a brother?

a) 3
b) 12
c) 15
d) 27

Answer 1

To find the number of people who have both a sister and a brother, we need to find the intersection of the two groups. The number of people who have both a sister and a brother is 27.

Step-by-step explanation:

To find the number of people who have both a sister and a brother, we need to find the intersection of the two groups. The group of 30 people can be represented as the universal set U. The set of people who have sisters can be represented as A and the set of people who have brothers can be represented as B. We know that |A| = 12 and |B| = 15.

We can find the number of people who have both sisters and brothers by finding the intersection of A and B, which can be represented as A ∩ B. We can use the formula |A ∩ B| = |A| + |B| - |A U B|. Since there are 30 people in total (U), we have |A U B| = |U| = 30.

Therefore, |A ∩ B| = |A| + |B| - |A U B| = 12 + 15 - 30 = 27.