NP-hard proof with reduction from two known NP-hard problems As I understand, to show that a certain problem P is NP-hard we can reduce a known NP-hard problem, Q, to problem in P in polynomial time. To show that the problem P is NP-hard in strong sense, we can reduce a know NP-hard problem Q to problem P in pseudo polynomial time.
Is it possible to show that a certain problem P is NP-hard by reducing two known NP-hard problems Q and Q' to a problem in P?
If you can reduce one NP-hard problem to a problem&nbsp;$L$, then $L$&nbsp;is NP-hard. If you can reduce a second NP-hard problem to&nbsp;$L$, then so what? You already know that $L$&nbsp;is NP-hard. How could reducing more problems to&nbsp;$L$ make $L$ easier (e.g., not NP-hard)?

It's like saying, "If I have one million dollars, I'm rich. If I have two million dollars, am I still rich?"