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If grammar is an $LL(1)$ and does not contain any null production (i.e $V \rightarrow \epsilon$) then does that grammar necessarily be an $LR(0)$ grammar?

I have tried to find counterexample for above statement but was unable to find one.

If above statement is valid please provide (idea of) proof or reference to proof. If the statement is wrong please provide a counterexample.

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