# Languages A, B ∈ NP-complete such that A⋃B = Σ*

I’m pretty new to complexity theory and it seems like I stuck with this problem. We should find language $$B$$ such that it accepts any words rejected by $$A$$ but in that case, it seems that $$B$$ is a complement of $$A$$ and therefore $$B$$ belongs to $$coNPC$$. What is my mistake? Thank you!