1. The problem asks to identify which option is NOT a valid proof technique. 2. Let's analyze each option: a. Direct proof: This is a valid proof technique where we start from known facts and use logical steps to arrive at the conclusion. b. Mathematical induction: This is a valid proof technique used especially for statements involving natural numbers. c. Empirical proof by finite examples alone: This is NOT a valid proof technique because proving a statement true by checking only a finite number of cases does not guarantee it holds in general. d. Proof by contradiction: This is a valid proof technique where we assume the negation of the statement and derive a contradiction. 3. Therefore, the answer is option c: Empirical proof by finite examples alone is NOT a valid proof technique.