### Logic and Proof

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

^{1}, 2

^{2}, 2

^{3},... 2

^{n}

- 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.

## 2 Comments:

Well done John. Way to take responsibility.

11:41 AM

Way to go John. Way to take responsibility.

11:41 AM

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