Expert: Paul Klarreich - 8/21/2011

Question
Hi, Paul. It's Susan, again. I just sent you an email, and I forgot to include these 2 problems. I just need to know if my answers are correct.

Problem 1:
Determine if the argument is valid or invalid.

If the bell rings, then we answer the door.
The bell rings.
We answer the door.

1. Valid by the law of detachment
2. Valid by the law of contraposition
3. Invalid by fallacy of the converse
4. Invalid by fallacy of the inverse
5. Valid by the law of syllogism
6. Valid by disjunctive syllogism

My answer:
1. Valid by the law of detachment (I was a little unsure, though, because my friend chose Valid by the law of syllogism. I think I am right, but not sure completely)

Problem 2:
Identify which argument is invalid.
     
1. Either the panda yawns or she is alert.
The panda did not yawn.
Therefore, she is alert.

     
2. If the panda yawns, then she is not alert.
The panda is not alert.
Therefore, she yawned.

     
3. If Tom is cooking, then I am not hungry.
I am hungry.
Therefore, Tom is not cooking.

     
4. If it is hailing, then I will not go outdoors.
If I will not go outdoors, I will not raise any money for charity.
Therefore, if it is hailing, then I will not raise any money for charity

     
5. If it is hailing, then I am not going outdoors.
It is hailing.
Therefore, I am not going outdoors.

My answer:
I chose 2. If the panda yawns, then she is not alert.
The panda is not alert.
Therefore, she yawned.

Sorry if I am a bother, but I'm just trying to keep my grades up. Thank you!

Answer
Questioner:Miss Susan Wilson
Country:Texas, United States
Category:Advanced Math
Private:No

Question:Hi, Paul. It's Susan, again. I just sent you an email, and I forgot to include
these 2 problems. I just need to know if my answers are correct.

Problem 1:
Determine if the argument is valid or invalid.

If the bell rings, then we answer the door.
The bell rings.
We answer the door.

1. Valid by the law of detachment
2. Valid by the law of contraposition
3. Invalid by fallacy of the converse
4. Invalid by fallacy of the inverse
5. Valid by the law of syllogism
6. Valid by disjunctive syllogism

..................................................
Here is what you have to do:  For each of those, you must write out the law in
symbolic form.  Each will be a tautology form. (not the fallacies, of course)  
Then symbolize the argument and see which it matches.

Now here you are using some vocabulary that is unfamiliar. (6, for example.)
But I think that:

1. is:  ((p -> q) and p) -> q.  [You should check by TT that this is a tautology.]

5. is:  ((p -> q) and (q -> r)) -> (p -> r)  [likewise]

Now assign p and q to the simple sentences in the exercise.  Which of these forms matches?

My answer:
1. Valid by the law of detachment (I was a little unsure, though, because my
friend chose Valid by the law of syllogism. I think I am right, but not sure
completely)

Problem 2:
Identify which argument is invalid.
    
1. Either the panda yawns or she is alert.
The panda did not yawn.
Therefore, she is alert.

     
2. If the panda yawns, then she is not alert.
The panda is not alert.
Therefore, she yawned.

     
3. If Tom is cooking, then I am not hungry.
I am hungry.
Therefore, Tom is not cooking.

     
4. If it is hailing, then I will not go outdoors.
If I will not go outdoors, I will not raise any money for charity.
Therefore, if it is hailing, then I will not raise any money for charity

     
5. If it is hailing, then I am not going outdoors.
It is hailing.
Therefore, I am not going outdoors.

My answer:
I chose 2. If the panda yawns, then she is not alert.
The panda is not alert.
Therefore, she yawned.

>>>>>>>>>>>>>>> Yes, this is correct, but you should state exactly why each of
the others is valid. (if you want full credit, that is)

Sorry if I am a bother, but I'm just trying to keep my grades up. Thank you!