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Unformatted text preview: S ⊆ A having odd cardinality is 2 n-1 . Prove your answer by induction. 5. (GRE Problem 69, Page 46) Let T denote a nonempty binary tree in which every node is a leaf or has two children. Then n ( T ) denotes the number of non-leaf nodes of T (where n ( T ) = 0 if T is a leaf), h ( T ) denotes the height of T (where h ( T ) = 0 if T is a leaf), T L denotes the left subtree of T and T R denotes the right subtree of T . If F is a function deﬁned by F ( T ) = ‰ if T is a leaf F ( T L ) + F ( T R ) + min( h ( T L ) ,h ( T R )) otherwise then show F ( T ) = n ( T )-h ( T ) by induction....
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- Spring '12
- Natural number, Prime number