# How to prove coNP is closed under reverse Karp Reduction?

Is it true that $$A \leq_k B \land B \in \mathsf{coNP} \implies A \in \mathsf{coNP}$$?

If so, how would you go about proving it?

• Use the definitions. – Yuval Filmus Apr 9 at 5:05
• @YuvalFilmus do you honestly believe your comment has any value whatsoever? – Zarwan Apr 9 at 5:58
• @Zarwan Definitely. It has worked in the past several times. – Yuval Filmus Apr 9 at 6:03
• @sargeras, does this answer ring a bell? – Apass.Jack Apr 9 at 6:15
• @Apass.Jack Yes that actually does help. I wasn't initially sure if $A \leq_{k} B \implies \overline{A} \leq_{k} \overline{B}$ holds. Thanks! – sargeras Apr 9 at 20:44