Proof By Counter Example

Not necessarily a formal proof. Used for disproving Conditional Statement by finding a value $C$ for condition $P$ that results in a Proof By Contradiction.

• First, prove that your value $C$ exists in the set that you defined it in
• Then, prove that $C$ satisfies the condition in the Conditional Statement
• Then, prove that $P$ is false, thereby proving Proof By Contradiction

Proof Format

$A⟹B$

1. Choose $x$ that is in the interval
2. Prove that $x$ is inside the interval
3. Prove that A is true, and B is false OR:
4. Write you WTS in a statement that has the negated result of the initial statement. Make sure the WTS includes a $\exists$ for your values that you want to choose for. $\exists x\in I,A⟹\neg B$
5. Choose $x$ that is in the interval
6. Prove that $x$ is inside the interval
7. Prove that A is true, and B is true OR:
8. Negate the statement
9. Find a value x that fufills that negated statement