Is the following line true?
Consider three problems A, B and C. If $A$ $<p$ $B$ and $B$ $<p$ $C$ and $B$ is NP-complete problem, then $C$ is also NP-complete.
If B is NP-complete, then C would have also been NP-complete if it was in NP but it is not given here. Can we consider it false? Or is there any other reason?