Let M(x, y) be the statement “x is a mother of y”, where the universe of discourse is the set of all people in the world.
Express the statement "A person’s mother’s mother cannot be his/her mother."
I have come up with two solutions and they seem to be the same to be. I can't see the differences in results for both.
- ∀x∃y∃z(M(y,x)∧ M(z,y) ∧ ¬M(z,x)
- ∀x∃y∃z((M(y,x)∧M(z,y)) -> ¬M(z,x))