True or False questions. Simply write $$T$$ or $$F$$ in front of each statement.

$\_\_\_\_\_(1)$ If a problem X belongs to NP$-$hard, it$$s impossible that X can be solved by a polynomial algorithm.

$\_\_\_\_\_(2)$ For any problem in NP category, its polynomial approximation algorithm always exist. $\_\_\_\_\_(3)$ If a problem A can be reduced to a problem B$,$ then the inverse$($reverse$)$ reduction from B to A

also exists.

$\_\_\_\_\_(4)$ Some NPC problems cannot be verified in polynomial time.

$\_\_\_\_\_(5)$ If P is equal to NP$,$ then all NP$-$hard problems can be resolved in polynomial time.

$\_\_\_\_\_(6)$ If one problem in NP category can be resolved in polynomial time, then all NP problems can be solved in polynomial time.

$\_\_\_\_\_(7)$ If a problem X can be solved by an exponential algorithm, then it$$s impossible to reduce X to a problem Y where Y is in category P$.$

$\_\_\_\_\_(8)$ The running time complexity of an algorithm is always independent of the input data structure. $\_\_\_\_\_(9)$ If an algorithm does not require any input data, it$$s impossible to analyze its running time

complexity.

$\_\_\_\_\_(10)$ If algorithm X consistently has a larger approximation ratio than algorithm Y for the same problem in all cases and conditions, then the running time complexity of algorithm Y must be higher than that of algorithm X in the worst$-$case scenario.