Two languages such that $L_1 \cup L_2 \leq_m\, L_1 \cap L_2$ and two (other?) such that $L_1 \cap L_2 ≤_m\, L_1 \cup L_2$?

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Are there languages $L_1$, $L_2$ such that such that $$L_1 \cup L_2\leq_m\, L_1\cap L_2,$$ and two other languages such that $$L_1 \cap L_2 \leq_m\, L_1 \cup L_2?$$ And if so, what are they? How can i go about finding these?