Let $$L_1$$ be regular language, $$L_2$$ be a deterministic context free language and $$L_3$$ a recursively enumerable language, but not recursive. Which one of the following statements is false?
$$L_3 \cap L_1$$ is recursive
$$L_1 \cap L_2 \cap L_3$$ is recursive enumerable
$$L_1 \cup L_2$$ is context free
$$L_1 \cap L_2$$ is context free
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