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Hint: let $A$ be a NP-complete language and $B=\Sigma^*$. Then $A \cup B = \Sigma^*$. Is $B$ the complement of $A$? Does it belong to coNPC?
Hint: let $A$ be a NP-complete language and $B=\Sigma^*$. Then $A \cup B = \Sigma^*$. Is $B$ the complement of $A$?
