Hypothesis/Conclusion
Symbols
Mixed Bag
C.I.C.
Laws
100
Hypothesis of "If elephants fly, then fish don't swim."
elephants fly
100
"If you get back late, then Mom will be mad" q V p
Mom will be mad or you get back late
100
Counterexample for "If it is a day of the week, then it is Thursday."
Sun, Mon, Tues, Wed, Fri, Sat
100
Converse of If it rains, then I stay home.
If I stay home, then it rains.
100
1) p ---> q
2) ~ q
3) ~ p
Law of Contrapositive
200
Conclusion of "If elephants fly, then fish don't swim."
fish don't swim
200
"If you get back late, then Mom will be mad p <---> q
You get back late if and only if Mom will be mad
200
2 ways to say biconditional: If pigs fly, then dolphins swim.
pigs fly if and only if dolphins swim
dolphins swim if and only if pigs fly
200
Inverse of If it rains, then I stay home.
If it does not rain, then I do not stay home.
200
1) p ---> q
2) q ---> r
3) p ---> r
Law of Syllogism
300
p of "If Tania is tired, then she takes a nap."
Tania is tired
300
"If you get back late, then Mom will be mad ~q
Mom will not be mad
300
Therefore
300
Contrapositive of If it rains, then I stay home.
If I do not stay home, then it does not rain.
300
Law & Conclusion
1) If a dog has fleas, then it scratches
2) Rover has fleas
Detachment & Rover/it scratches
400
q of "If Tania is tired, then she takes a nap."
she takes a nap
400
"If you get back late, then Mom will be mad" You get back late and Mom is not mad.
p ^ ~ q
400
What statement (2) is needed to have the Law of Detatchment? If an animal is a frog, then it has two legs.
An animal is a frog.
400
q ---> p
Converse
400
Law & Conclusion
1) If a don't wear a sweater, then I'll get a cold.
2) I don't get a cold.
Contrapositive & I wear a sweater
500
Hypothesis of JKL -----> MNO
JKL
500
"If you get back late, then Mom will be mad" Mom is mad or you did not get back late.
q V ~ p
500
Inverse
"If I stay at home, then I do not pitch at the game."
If I do not stay at home, then I do pitch at the game
500
~ p ---> ~ q
Inverse
500
Law & Conclusion
1) If a dog has fleas, then it scratches
2) Rover scratches
Invalid/No conclusion