# is this argument valid?

• Dec 11th 2008, 01:16 PM
ana1808
is this argument valid?
(Hi)
some dogs hate cats
all dogs have fleas
frodo has fleas and hates cats
----------------------------
therefore Frodo is a dog

is it valid ? and why?

the explanation should be something like "if P then Q "............
• Dec 11th 2008, 02:32 PM
Greengoblin
No, because "some dogs hate cats" doesn't exclude other species from the hating of cats, and "all dogs have fleas", doesn't exclude others from having fleas, so while Frodo is likely a dog, it's not certain.
• Dec 12th 2008, 08:00 PM
Soroban
Hello, ana18081

It is not valid.
I have a Venn diagram proof.

Quote:

Some dogs hate cats
All dogs have fleas
Frodo has fleas and hates cats
----------------------------
Therefore: Frodo is a dog

Is it valid? Why or why not?

"All dogs have fleas."

There is a set of all dogs.
There is a set of all things that have fleas.
. . $\{\text{dogs}\}\:\subset\: \{\text{have fleas}\}$

The Venn diagram looks like this . . .
Code:

      * - - - - - - - - - - - - - - - - - *       | Has fleas                        |       |      * - - - - - - - - - *      |       |      |                  |      |       |      |      Dogs        |      |              |      |                  |      |       |      |                  |      |       |      * - - - - - - - - - *      |       |                                  |       * - - - - - - - - - - - - - - - - - *

"Some dogs hate cats."

There is a set of all things that hate cats.

The set of "Dogs" and the set of "Hate Cats" do intersect.

The Venn diagram looks like this:
Code:

      * - - - - - - - - - - - - - - - - - *       | Has fleas                        |       |      * - - - - - - - - - *      |       |      | Dogs              |      |       |      |      * - - - - - + - - - + - - - *       |      |      |          |      |      |       |      |      |    X    |      |      |       |      * - - - + - - - - - *      |      |       |              |                  |      |       * - - - - - - - + - - - - - - - - - *      |                       |                Hates cats |                       * - - - - - - - - - - - - - *
There is at least one creature which is a dog and hates cats.

"Frodo has fleas and hates cats."

He could be in the section with the "X"
. . but he also could be in the shaded region.
Code:

      * - - - - - - - - - - - - - - - - - *       | Has fleas                        |       |      * - - - - - - - - - *      |       |      | Dogs              |      |       |      |      * - - - - - + - - - + - - - *       |      |      |          |///////|      |       |      |      |    X    |///////|      |       |      * - - - + - - - - - *///////|      |       |              |///////////////////|      |       * - - - - - - - + - - - - - - - - - *      |                       |                Hates cats |                       * - - - - - - - - - - - - - *

Therefore, we can not conclude that Frodo is a dog.

• Dec 12th 2008, 11:02 PM
CaptainBlack
Quote:

Originally Posted by ana1808
(Hi)
some dogs hate cats
all dogs have fleas
frodo has fleas and hates cats
----------------------------
therefore Frodo is a dog

is it valid ? and why?

the explanation should be something like "if P then Q "............

A single counter example will demonstrate that the argument is invalid, so the possibility of existence of a flea infested cat hating hobbit named frodo will prove the argument invalid.

CB