Thread: Logic question

I am given the following premises and asked to derive a formal conclusion and then state the conclusion.

1. No terriers wander among the signs of the zodiac.
2. Nothing that does not wander among the signs of the zodiac is a comet.
3. Nothing but a terrier has a curly tail.

So from c. we can clearly say that if you have a curly tail, you do not wander among the signs of the zodiac. But I can not infer anything from b because...

b says..

-Anything that wanders among the signs of the zodiac is a comet

-If wander, then comet
P then Q

a. implies ~P, but we can not imply ~q from ~p

So is the only conclusion I can form about these premises be....

- if you have a curly tail, you do not wander among the signs of the zodiac?

Thanks for any help you can provide.

Hello, ehpoc!

I am given the following premises and asked to derive a formal conclusion
and then state the conclusion.

. . (a) No terriers wander among the signs of the zodiac.
. . (b) Nothing that does not wander among the signs of the zodiac is a comet.
. . (c)Nothing but a terrier has a curly tail.

(a) says: If is a terrier, then does not wander among the signs.
. . .

(b) says: If does not wander, then is not a comet.
. . .

(c) says: If has a curly tail, then is a terrier.
. . .


We have: .


By the Law of Syllogism: .

Therefore: if has a curly tail, then is not a comet.