Let us consider the binary trees below.

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Select one or more:a$.$ For tree a$),$ if we remove node D$,$ then the tree does no longer have the AVL property.b$.$ For a binary tree that does have the AVL property. If the property is violated after inserting one node, then the property can be restored using an algorithm $($based on rotations$)$ that runs in constant time cost.c$.$ For tree a$),$ if we remove node C$,$ then the tree does no longer have the AVL property.d$.$ Both trees a$)$ and b$)$ have the AVL $($height$-$balanced $1-$tree$)$ property.e$.$ Tree in b$)$ will not have the AVL property, if a right child is added to node A$.$