Proof

• A statement that has been proven is called a theorem.
• A statement that has yet to be proven is called a conjecture.
• Proof by deduction starts from facts or definitions then uses logical steps to reach the desired conclusion.
• To prove an identity, start with the expression on one side of the identity and manipulate it until it matches the other side.
• Proof by exhaustion involves showing that every option is true in a statement. If any option is false, then the whole statement is false.
• Proof by counter example uses one example that doesn't work for the statement, disproving the whole statement.
• Proof by contradiction assumes the opposite result is true and then use the same process of proof by deduction to reach the conclusion that the assumption is incorrect.