Converse
If a child is 5 years old, then they are in kindergarden.
"If a child is in kindergarden, then they are 5 years old"
If you like tennis, then you play on the tennis team.
"If you do not play on the tennis team, then you do not like tennis"
If x is odd, then 3x is odd.
"If x is not odd, then 3x is not odd"
Reasoning that uses patterns
What is INDUCTIVE reasoning
If there is snow on the ground, flowers are not in bloom.
"If flowers are not in bloom, then there is snow on the ground."
If x is odd, then 2x is even.
"If 2x is not even, then x is not odd."
If you like hockey, then you will go to the hockey game.
"If you do not like hockey, then you will not go to the hockey game."
If I get an A on this test, then my mom will give me $5.
I got an A on the test. What conclusion can be made?
My mom will give me $5.
(Law of Detachment)
If 2 lines intersect, then they cross each other.
"If 2 lines cross each other, then they intersect."
If a point lies on 2 lines, then it is at the intersection.
"If a point is not at the intersection, then it does not lie on 2 lines."
If you visited the White House, then you've been to Washington D.C.
"If you have not visited the White House, then you have not been to Washington D.C."
If it is a small hot planet, then it is Mercury.
If the planet is the closest to the sun, then it is a small hot planet.
What conclusion can you make?
If the planet is the closest to the sun, then it is Mercury.
(Law of Syllogism)
If it is snowing, then it is cold. Is the converse of this statement true or false, and why?
"If it is cold, then it is snowing." FALSE - it can be cold without snowing
If you like purple, then you love Barney.
"If you do not love Barney, then you do not like purple."
If you are 16, then you can legally drive. Is the inverse of this statement true or false, and why?
"If you are not 16, then you can not legally drive." FALSE - those older than 16 can also legally drive
100, 200, 300, 400, 500,...
The next number is 600
What type of reasoning is used?
What is Inductive Reasoning?
(using a pattern)
What is the mathematical notation for the converse? (Hint: The regular conditional is notated p --> q)
q --> p
What is the mathematical notation for the contrapositive? (Hint: A regular conditional is noted p --> q)
~q --> ~p
What is the mathematical notation for inverse? (Hint: The regular conditional is notated p --> q)
~p --> ~q
f(x)=3x-1
f(5)=14
What type of reasoning is used?
What is Deductive Reasoning?
(using a rule property or definition)