$(15\%)$ Answer True or False for the following statements and also justify your reasons.

$(3\%)$ If an NP$-$complete problem can be reduced to a problem $L$ in polynomial time, then $L$ is NP$-$

complete.

$(3\%)$ If a problem A can be reduced to a problem $B$ and AinP, then BinP.

$(3\%)$ If a problem AinP, then AinNP.

$(3\%)$ If $PNP,$ there exists a $2-$approximation algorithm for the general traveling$-$salesman problem.

$(3\%)$ The maximum numbers of elements in a heap of height $h$ is $2^h-1.$