# Really confused

Suppose there is a language L∈NP, that is not NP-Complete and L≠∅ and L≠Σ∗. Which of the following statements can we infer from this?

P = NP

P ⊊ NP

P ≠ NP

NP ⊆ P

• – D.W.
Aug 13, 2021 at 17:04

What would happen if $$P=NP$$? Clearly $$P$$-complete $$=P$$, and hence also $$NP$$-complete = $$NP$$. This means that every language in $$NP$$ would also be in $$NP$$-complete. So finding a language that isn't $$NP$$-complete, means that we must have $$P\neq NP$$