Question
Explain Why one of these statements is true and the other is false:
\begin{align*} (\forall \text{ man } M)(\exists \text{ woman } W) \mid W \text{ is the mother of } M \\ (\exists \text{ woman } W)(\forall \text{ man } M) \mid W \text{ is the mother of } M \end{align*}
Answer
The first statement is true, and the second is false because every man has a mother but there doesn’t exist a woman who is the mother of all men.