Problem #PRU-117001

Problems Discrete Mathematics Set theory and logic Mathematical logic Mathematical logic (other)

Problem

In the family of happy gnomes there is a father, a mother and a child. The names of the family members: Alex, Charlie and Jo. At the dinner table two gnomes made two statements.

Charlie said: “Alex and Jo are of different genders. Alex and Charlie are my parents”.

Alex said: “I am Jo’s father. I am the daughter of Charlie”.

Who is who? That is, what is the name of the father, the mother and the child, if it is known that each gnome lied once, and each told the truth once.