Six members of a family namely $A$, $B$, $C$, $D$, $E$, and $F$ are travelling together. $B$ is the son of $C$ but $C$ is not the mother of $B$. $A$ and $C$ are a married couple. $E$ is the brother of $C$. $D$ is the daughter of $A$. $F$ is the brother of $B$. How many male members are there in the family?

Let us identify the gender and relationships of each member ($+$ for male, $-$ for female):
1. "$B$ is the son of $C$ ": $B$ is Male ($+$).
2. "$C$ is not the mother of $B$ ": Since $C$ is a parent but not the mother, $C$ must be the father. $C$ is Male ($+$).
3. "$A$ and $C$ are a married couple": Since $C$ is male, $A$ must be the wife. $A$ is Female ($-$).
4. "$E$ is the brother of $C$ ": $E$ is Male ($+$).
5. "$D$ is the daughter of $A$ ": $D$ is Female ($-$).
6. "$F$ is the brother of $B$ ": $F$ is Male ($+$).

Let's count the male members ($+$): $B,C,E,F$.
Total number of male members $=4$.