# Reduction over intersection of languages

Given two languages $L1$ and $L2$, such that $L2$ is NP-Hard under polytime (many-one or Turing) reduction. Let $L=L1\cap L2$.

1- Is it true that if $L2$ is polytime (many-one or Turing) reducible to a third language $L3$, then $L$ is polytime reducible to $L1\cap L3$ ?

2- If $L \in$ P, what can it be concluded about the complexity of $L1$ ?

-