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

Monday, May 01, 2006

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.
If two points are placed on the circumference of a circle and joined by a chord, you'll get two regions.

*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 21, 22, 23,... 2n
  • 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.
*In deductive reasoning, we make a statement that we are absolutely certain is true based on TRUE STATEMENTS.

ex. Add 2 odd numbers.
1 + 3 = 4
5 + 7 = 12
9 + 11 = 20
  • Sum is always even?
Odd numbers:
2x + 1, 2y + 1
  • 2x + 1 + 2y + 1
  • 2x + 2y + 2
  • 2(x + y + 1)
* 2 is a factor, therefore sum is always even.

ex

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

2 Comments:

Blogger Mr. Malandrakis said...

Well done John. Way to take responsibility.

11:41 AM

 
Blogger Mr. Malandrakis said...

Way to go John. Way to take responsibility.

11:41 AM

 

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