Which of the following statements is false?

a$.$

In preorder traversal, initially the root node is visited and then the same operation is repeated for each subtree that are rooted at the children of root node.

b$.$

During an inorder traversal, we visit a position between the recursive traversals of its left and right subtrees.

c$.$

The height of a nonempty tree is equal to the maximum of the depths of its leaf positions.

d$.$

A breadth$-$first traversal is a common approach used in software for playing games.

e$.$

A binary tree is improper if each node has either zero or two children.