Which one of the following expressions represents the above statement?

Let the specific person mentioned in the statement be represented by the variable $y$.

1. "There is a person...": This translates to an existential quantifier $\exists y$.

2. "...who does not know anyone else": For any other person $x$ (where $x \neq y$), person $y$ does not know $x$, which is represented as $

eg M(y, x)$.

3. "...but that person is known by everyone else": For any other person $x$ (where $x \neq y$), person $x$ knows $y$, which is represented as $M(x, y)$.

Combining both conditions for every person $x$ distinct from $y$: $$\forall x \big((x \neq y) \rightarrow (M(x, y) \wedge eg M(y, x))\big)$$

Adding the outer existential quantifier over $y$, we get: $$(\exists y)(\forall x)\big((x \neq y) \rightarrow (M(x, y) \wedge eg M(y, x))\big)$$

Hence, option A correctly represents the given statement.