Chapter 2.3, Problem 1E

Suppose a family contains two children of different ages, and we are interested in the gender of these children. Let F denote that a child is female and M that the child is male and let a pair such as FM denote that the older child is female and the younger is male. There are four points in the set S of possible observations:

$S=\left\{FF,FM,MF,MM\right\}.$

Let A denote the subset of possibilities containing no males; B, the subset containing two males; and C, the subset containing at least one male. List the elements of A, B, C, A ∩ B, A ∪ B, A ∩ C, A ∪ C, B ∩ C, B ∪ C, and $C\cap \bar{B}$.