Before 1/1/2010, the US and China are involved in a military conflict. For this Claim to be judged true, there must be an engagement of US/Chinese military forces, by land, air or sea, at the direction of military commanders and/or the respective governments. It is not necessary that both sides be engaged (for example a missle attack on a ship in which the other side does not return fire, or the unilateral firing of nuclear weapons).
This claim will be judged yes in the event of a) an official declaration of war on the part of the US or China towards the other country or b) officially reported military casualties of war on the part of either the US or China c) officially reported civilian casualties of war on the part either the US or China
The key here is officially reported causualties(i.e. I wouldn't count the type of casualties we saw during the "Cold War"). Casualties can be officially reported by the US, China or the UN. It is key here that the casualties must be reported by at least one side or the UN as intentional casualties of an act of war, not accidental deaths.
