Since $R$ is a domain, the product $ab$ is nonzero. Now, we have $ab \in I$ because $I$ is an ideal and $a \in I$, and similarly, $ab \in J$ because $J$ is an ideal and $b \in J$. Thus, $ab \in I \cap J$, and since $ab \neq 0$, we have $I \cap J \neq \{0\}$.
(ii)
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