# Math Help - Logic question

1. ## 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.

2. ## Re: Logic question

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 $x$ is a terrier, then $x$ does not wander among the signs.
. . . $\text{terrier} \to\; \sim\text{wander}$

(b) says: If $x$ does not wander, then $x$ is not a comet.
. . . $\sim\text{wander}\:\to\;\sim\text{comet}$

(c) says: If $x$ has a curly tail, then $x$ is a terrier.
. . . $\text{tail}\:\to\;\text{terrier}$

We have: . $\begin{bmatrix}(c) & \text{tail} &\to& \text{terrier} \\ (a) & \text{terrier} & \to & \sim\text{wander} \\ (b) & \sim\text{wander} &\to& \sim\text{comet} \end{bmatrix}$

By the Law of Syllogism: . $\text{tail}\:\to\;\sim\text{comet}$

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