Vocab
Inductive Reasoning
The process of reaching a conclusion based on a pattern.
If p, then q
Conditional
If I study hard, then I will get an A.
1-Change to converse
2-T/F and counter example
If I get an A, then I studied hard.
False- I could have cheated
Law of Detachment
If p-q is a true statement and p is true then q is true.
p-q (true)
p (true)
q (true)
If you are a cat, then you have 4 legs.
If you are a fish, then you have fins.
If you have 4 legs, then you are also a mammal.
Question- Karen is a cat. What else do we know about her?
Karen has 4 legs.
Conjecture
A educated guess based on known information and specific examples
If q, then p
Converse
If I study hard, then I will get an A.
1- Change to Inverse.
2-T/F and counter example
If I do not study hard, then I will not get an A.
False-, I could understand it without knowing I do.
Law of Syllogism
If p-q and q-r are true statements, then p-r is a true statement.
p-q (true) & q-r (true)
=
p-r (true)
If you play girls basketball, then you have blonde hair.
If you play girls softball, then you have black hair.
If you have blonde hair, then your favorite color is blue
Question- Lakelyn plays girls softball. What else?
Lakelyn has black hair.
Counter Example
An example that contradicts the conjecture showing that the conjecture is not always true
If not p, then not q
Inverse
If I study hard, then I will get an A.
1- Change to contrapositive.
2-T/F and counter example
If I do not get an A, then I did not study hard.
True
Which law is this?
If he studies, then he will get good grades. If he gets good grades, then his parents will be proud.
Law of Syllogism
If you are a cat, then you have 4 legs.
If you are a fish, then you have fins.
If you have 4 legs, then you are also a mammal.
Question- T or F, if you have four legs you are also a cat. Why or why not?
False, you cannot go back.
Deductive Reasoning
The process of reaching a specific valid conclusion based on general facts, rules, definitions, or properties
If not q, then not p
Contrapositive
If I study hard, then I will get an A.
1- Change to biconditional.
2-T/F and counter example
I will study hard if and only if I will get an A.
False, you can't know your grade before you study.
Which law is this?
If she runs a mile, then she will be tired after.
Law of Detachment
If you play girls basketball, then you have blonde hair.
If you play girls softball, then you have black hair.
If you have blonde hair, then your favorite color is blue
Question- T or F If you play basketball and have blonde hair, your favorite color is blue also. Why or Why not?
q-r is true, then p-r is true.
Valid Argument
An argument is valid if it is impossible for all the premise or supporting statements of the argument to be true and it's conclusion is false
P if and only if q
Biconditional
p: all dogs have ears
q: all cats have whiskers
r: all fish have fins
Question- change to p^r
All dogs have ears and all cats have whiskers.
What law is this?
If it is Monday, then I have school. If I have school, then I have math class.
Law of Syllogism
p: all frogs jump
q: all fish swim
r: all birds chirp
Question- Change to p v ~q
All frogs jump or not all fish swim.