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If I have two decidable languages $A$ and $B$, is $A \leq_m B$ true? How would I show this?

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    $\begingroup$ What if $B = \emptyset$? $\endgroup$ Oct 20, 2020 at 23:03

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That is false. Consider for example the alphabet $\Sigma = \{0,1\}$ and the two languages $A = \emptyset$ and $B = \Sigma^*$.

Clearly both $A$ and $B$ are decidable (by the trivial algorithms that always reject and always acccept, respectively) but it is false that $A \le_m B$.

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