Existence, Uniqueness and Counterexamples · Hard problem

Let $S = \{1, 2, 3, 4, 5, 6\}$, with all variables in $S$. How many of these four statements are true? (a) $\forall x\ \exists y: x + y = 7$. (b) $\exists y\ \forall x: x + y \le 7$. (c) $\forall x\ \exists y: y \ne 1$ and $xy \in S$. (d) $\exists y\ \forall x: y \ne 1$ and $y \mid x$.