Let $T$ be an arbitrary binary tree with $n$ nodes. For each node $x$ in $T$ let us define $w(x)$ as the number of descendants of $x,$ including $x$ itself. So$,w(x)$ is $n$ if $x$ is the root and it is $1$ if $x$ is a leaf node in $T.$ Now let us define $W(T)$ to be the sum of $w(x)$ over all nodes $x$ in $T.$ We want to determine tight asymptotic lower and upper bounds on $W(T)$ based on the structural shape of $T.$ These bounds can be expressed as functions of $n.$ W$($T$)$ can be as low as $?)$ and as high as $?).$

a$.LB(n)=(n)$ and $UB(n)=(nlogn).$

b$.LB(n)=(n)$ and $UB(n)=(n^2).$

c$.LB(n)=(nlogn)$ and $UB(n)=(nlogn).$

d$.$ None of the other choices.

e$.LB(n)=(nlogn)$ and $UB(n)=(n^2).$