Disprove by Counter Example or Prove each of the following :

1. $\forall a,b,c \in Z, a \vert b \wedge a \vert c \rightarrow a\vert bc$
2. $\forall a,b,c \in Z, a \not \vert b \wedge a \not \vert c \rightarrow a \not \vert bc$
3. $\forall q,r \in Q, qr \in Q$
4. $\forall a \in Q, a \not \in Z \rightarrow (\lfloor a \rfloor \neq \lceil a \rceil)$
5. $\forall a,b,c \in Z, a \vert b \vee a \vert c \rightarrow a\vert bc$
6. $\forall a,b \in Z, a \not \vert b^2 \rightarrow a \not \vert b$

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