### Today's post

*MAY 4, 2006*

# COUNTER EXAMPLES

**Today's lesson is**

*COUNTER EXAMPLES.*It is about proving the CONJECTURE (*conjecture:*statement made by examples) wrong by providing true statements, examples, diagrams, equations. This lesson is somehow easy because all you do is prove that the conjecture is wrong. However, such conjectures may lead to sudden confusion because sometimes it gives just a small possibility of proving it wrong. You REALLY have to think about it too.**Here are some examples:**

*1) The sum of 2 prime numbers is always even.*(CONJECTURE)**examples that verify this conjecture:**

**3 + 5 = 8**

*even***7 + 9 = 16**

*even***11 + 13 = 24**

*even*

**examples that contradict this conjecture:**

**7 + 2 = 9**

*odd***11 + 2 = 13**

*odd***13 + 2 = 15**

*odd*

**2) The expression 1 / x will always be less than 1 for any value of x.**

**examples that verify the conjecture:**

**x = 2**

**1 / 2 = 0.5**

**x = 4**

**1 / 4 = 0.25**

**examples that contradict the conjecture:**

**x = 1**

**1 / 1 = 1**

**x = 0.5**

**1 / 0.5 = 2**

**That's today's lesson. The homework is Exercise 48.**

*MAY 2, 2006**VENN DIAGRAMS*

*VENN DIAGRAMS*

*LESSON LAST TUESDAY:*

**EXAMPLES**

**A upside down U B = m, u**

**( B \ A ) ' = o, p, s, m, u, r**

**A \ B = o, p, s**

**( A U B ) ' = r**

## 3 Comments:

Wow, Vince. Just wow. You rocked my socks off. That post was so cool.

5:48 PM

Vince, this is an absolutely amazing post. Fantastic job to set an example.

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