Problem $1(3$ points$)$

For each of the following statements about red$-$black trees, determine whether it is true or

false. If you think it is true, provide a justification. If you think it is false, give a

counterexample.

$1)$ A subtree of a red$-$black tree is itself a red$-$black tree.

$2)$ The sibling of an external node is either external or it is a red.

$3)$ Given a red$-$black tree T$,$ there is a unique $(2,4)$ tree T$$ associated with T$.$

$4)$ Given a $(2,4)$ tree T$,$ there is a unique red$-$black tree T$$ associated with T