[BTM]

Helping my GF with some homework and ran into something I'm not totally sure about - symbolic arguments. I'm pretty comfortable with determining argument validity but don't know the definitions of the arguments. My thoughts are in parentheses.

Directions:
Name the type of symbolic argument (detachment, converse, inverse, contrapositive, syllogism) Indicate if it is valid or invalid.

1. If SF 49ers lose, Dallas Cowboys win. If Dallas Cowboys win, Texas declares a holiday. Therefore if SF 49ers lose, Texas declares a holiday.

(detachment, valid)

2. If you use MobileOil your car runs fast. Chet's car runs fast. Therefore he uses MobileOil.

(syllogism, invalid)

3. All dogs are animals (if you are a dog then you are an animal). Pluto is a dog. Therefore Pluto is an animal.

(converse, valid)

4. All cats are animals. Hillary is not an animal. Therefore Hillary is not a cat.

(contrapositive, valid)

5. If you save money, you will become rich. Mary does not save money, therefore she is not rich.

(inverse, invalid)

Thanks for looking

[Crimson92]

this is math?

wtf happend to 2+2=4????

[OMID INC]

oh gosh reminding me of the LSAT .. no!!!!!

[BTM]

Another snafu on a truth table, is this right for [(p->q) AND q] -> p

p....q....p->q..AND...q..->...p
T....T......T............T........T
T....F......F............F.........F
F....T......T............F.........T
F.....F......T...........F..........T

[Crimson92]

my brain hurts now

[Buegie]

the validity for each one seems to be correct. When I took this I think we used different names for the types of arguments though, so I can't help much with that.

[fdsasdasdf]

Originally Posted by BTM

Helping my GF with some homework and ran into something I'm not totally sure about - symbolic arguments. I'm pretty comfortable with determining argument validity but don't know the definitions of the arguments. My thoughts are in parentheses.

Directions:
Name the type of symbolic argument (detachment, converse, inverse, contrapositive, syllogism) Indicate if it is valid or invalid.

1. If SF 49ers lose, Dallas Cowboys win. If Dallas Cowboys win, Texas declares a holiday. Therefore if SF 49ers lose, Texas declares a holiday.

(detachment, valid)

2. If you use MobileOil your car runs fast. Chet's car runs fast. Therefore he uses MobileOil.

(syllogism, invalid)

3. All dogs are animals (if you are a dog then you are an animal). Pluto is a dog. Therefore Pluto is an animal.

(converse, valid)

4. All cats are animals. Hillary is not an animal. Therefore Hillary is not a cat.

(contrapositive, valid)

5. If you save money, you will become rich. Mary does not save money, therefore she is not rich.

(inverse, invalid)

Thanks for looking

All you need to know:

Law of Detachment:
All BMWs are fun to drive
Your car is a BMW
You can then conclude that your car is fun to drive since it is a BMW.

Syllogism:

Some A is B
All B is C
Therefore, some A is C

Contrapositive:

If P => Q, then ~Q => ~P
This is always true as long as P => Q is a valid statement.

Converse:

If P => Q, then Q => P

Converses are only true when:

P <=> Q

Truth table:

[(P => Q) AND Q ] => P

[P] [Q] [P => Q] [(P => Q) AND Q] [(Q => Q) AND Q => P]
T.....T.......T................T.................. ........T
T.....F.......F................F.................. .........T
F.....T.......T................T.................. .........F
F.....F.......T................F.................. .........T

Remember:

P => Q is false iff P is true and Q is false.

Oh, mathematical proofs class is fun, isn't it?

[radix]

1. syllogism, valid

2. converse, invalid

3. detachment, valid

4. contrapositive, valid

5. inverse, invalid

[JayKay335i]

The human genome is interesting.

[burningchicken]

lol isnt this from 10th grade?? well at least thats when I did it o.O

[escobar929]

Originally Posted by burningchicken

lol isnt this from 10th grade?? well at least thats when I did it o.O

10th grade? i did this in the 5th grade. 10th grade was trig for me

discrete math also goes into this, maybe its the intro part of the class