Suppose that the search for key $k$ in a binary search tree ends up in a leaf. Consider three sets: $A,$ the keys to the left of the search path; $B,$ the keys on the search path; and C $,$ the keys to the right of the search path. For example, if you take the final answer to problem $1$ and search for key $6,A=\{1\},B=\{5,7,6\},$ and $C=\{\}.$ Draw a counterexample to the following claim.

Claim: Any keys ainA,binB, and cinC must satisfy $ab,$ and $bc.$