Let us consider the binary trees below.

Select one or more:a$.$ For tree a$),$ if we add a left child to node $\backslash ($ C $\backslash ),$ then the tree does no longer have the AVL property.b$.$ Tree in b$)$ will not have the AVL property, if a left child is added to node Bc$.$ 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 linear time $\backslash ((\backslash$mathrm$\{$O$\}(\backslash$mathrm$\{$N$\})\backslash )$ where $\backslash ($ N $\backslash )$ is the number of nodes$).$d$.$ For tree a$),$ if we add a right child to node $\backslash ($ D $\backslash ),$ then the tree does no longer have the AVL property.e$.$ Tree in b$)$ will not have the AVL $($height$-$balanced $1-$tree$)$ property, if we remove node B