Law of Detachment
S1. If you eat your vegetables, then you can have desert
S2. You eat your vegetables
What is the 'if' part?
If you eat your vegetables
S1. If you study, you will pass the test
S2. If you pass, then you will celebrate
C. If you study, then you will celebrate
What do you need to find first in order to use deductive reasoning?
A general rule
What are the only two options truth Values can be?
True or false
S1. If it is raining, the soccer game will get cancelled
S2. It is raining
C. The soccer game will get cancelled
S1. If it is Saturday, then I will sleep in
C. If it is Saturday, I will have a great day
S2. If I sleep in, I will have a great day
The dress code says no hats, but The Big Y is wearing a hat.
The Big Y is breaking the dress code.
True or false: If x=y, then 3x+5=2y+y+8-3.
True
1. If x=5, then 2x=10
2. x=5
C: 2x=10
S1. If x=4, then y=8
S2. If y=8, then z=12
C. If x=4, then z=12
The Big Y got detention, because of that he missed cross country practice. The Big Y concludes that if you get detention, you cannot go to cross country practice. What is this?
Inductive reasoning, he starts with a specific scenario, then makes a general rule.
True or false: If you don't eat peanuts, then you are allergic to peanuts.
False
S1. If an angle is 90 degrees, then it is a right angle
C. Angle C is a right angle
S2. Angle C is 90 degrees
S1. If a shape is a square, then it has four sides
S2. If a shape is a rectangle, then it has four right angles
C. You cannot conclude anything because the conclusion of the first statement doesn't match with the hypothesis of the second statement.
If you use inductive reasoning, your conclusion will most likely be a guess, but when you use deductive reasoning, your conclusion will be . . .
A certainty
What about truth values gives a statement absolute clarity?
The power of binary simplicity.
S1. If you live in Miami, then you live in Florida
S2. The Big Y lives in Florida
C. Nothing because the 'then' part came before the 'if' part.
What is the difference between the law of detachment and the law of syllogism?
The law of detachment has one conditional statement and one fact, whereas the law of syllogism has 2 conditional statements that you can put into one.
All triangles have 3 sides. This shape has 3 sides. So it must be a triangle. True or false.
False, I never said that it was a polygon, it could have a curved side, or it could be open.
When using axiomatic independence, and you change a foundational rules value from true to false, what are you looking for?
To see if it breaks the rest of your math system or forms a new universe.