### Way to go!!!!

Way to go Vince!!!!! Fantastic double scribe post. Hopefully everyone can take a look at this and match your efforts in following posts. Keep up the great work!!!!

*This is a blog for my second semester pre-calculus 30s students. Have a blast!*

**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**

Just a quick note folks. I purposely haven't said anything in class about our scribe responsibilities over the past couple of weeks because there shouldn't be a need to. This is an enriched university entrance level course where standards and expectations are high. Everyone fully realizes that each day that there is a new lesson someone needs to be the scribe for that day. Even if it helps 1 or 2 people that night who might have been confused during the lesson then it's definitely served its purpose. Remember you are all responisble young adults and if the routine of scribing continues like it did for most of the course so far, everyone would only have to be the scribe every 21 classes (almost an actual month). Not a lot to ask for something which might make the world of difference to a few of your classmates, or possibly even people around the world taking the course. I've also noticed that it's the same group of 4 or 5 people who are always the "fill-in" scribes. The honus should be on everyone to put in their small part. Have a good day / night folks!!!

Logic and Proof: Inductive/Deductive Reasoning

If the same result occurs over again, we conclude it will always occur. This is called inductive reasoning.

ex. multiply and odd number by an even number

9 x 8 = 72

11 x 12 = 132

7 x 10 = 10

- From this, we can conclude that the products are all even. <-- We made a statement that is called a conjecture. A conjecture is something like an unproved theorem. Basically, we made a conjecture that says that all product of odd/even numbers are even.

*note: Having beyond 5 points made it difficult to count the regions, so I only did the first three examples.

*Conjecture: The number of regions follow the pattern 2

- The 6-sided polygon proves our conjecture wrong. Using our pattern, we should get 32 regions, but the 6-sided polygon only has 31 regions.

ex. Add 2 odd numbers.

1 + 3 = 4

5 + 7 = 12

9 + 11 = 20

- Sum is always even?

2x + 1, 2y + 1

- 2x + 1 + 2y + 1
- 2x + 2y + 2
- 2(x + y + 1)

ex

That's it for today's lesson. Homework is the Inductive and Deductive Reasoning worksheet and Exercise 45.