a logical question i tried to solve using VEN

[transgalactic]

data:
A.there are no grey bears
B.only polar bears are white

which of this following claims when added to the data leads us to the conclution
that all bears are a polar bears?

1.every non white bear is gray
2.all the polar bears are white
3.there are no black polar bears
4.each bear which is not a polar bear
is black

i tried to make a ven diagram
but i dont know whether i did it ok
or what to do next

http://img354.imageshack.us/my.php?image=16529534ax0.gif

[regor60]

data:
A.there are no grey bears
B.only polar bears are white

which of this following claims when added to the data leads us to the conclution
that all bears are a polar bears?

1.every non white bear is gray
2.all the polar bears are white
3.there are no black polar bears
4.each bear which is not a polar bear
is black

i tried to make a ven diagram
but i dont know whether i did it ok
or what to do next

http://img354.imageshack.us/my.php?image=16529534ax0.gif


You've categorized all white things as polar bears, which isn't correct. Of things that are white, only some are polar bears, and this should be reflected in an intersection between "white things" and "bears"

[davee123]

You've categorized all white things as polar bears, which isn't correct.

Actually, he's got it correct given the somewhat strange wording. It says "only polar bears are white", but it does not say "the only bears that are white are polar bears". The former would indicate that NOTHING else is white-- ONLY polar bears. So there's no white birds, white socks, white paper. Only white polar bears.

Actually, the wording also doesn't preclude non-white polar bears. IE, it says that the only bears which can be white (but aren't necessarily so) are polar bears. Hence, if you see a white bear, you be assured that it's a polar bear. But seeing a polar bear doesn't mean it's going to be white, and likewise seeing a green bear doesn't mean it's NOT a polar bear.

As for the OP:
1.every non white bear is gray

This means that since (for example) grizzly bears aren't polar bears, they CANNOT be white. And therefore, must be gray. However, we already know that no bears are gray, so grizzly bears cannot exist. In fact, the only things that can exist are white polar bears. So that's the answer they're looking for.

2.all the polar bears are white

See, here the meaning is that *all* polar bears are white, rather than just some. And that's fine-- it just tells us that there aren't any non-white polar bears. There could still be (say) brown grizzly bears.

3.there are no black polar bears

Ok. Now we know that polar bears can be any color except black. But it says nothing of our brown grizzly bear, who can still exist just fine.

4.each bear which is not a polar bear is black

Well, our brown grizzly bear can't exist, but a black one could. With this piece of information, we know that all non-polar bears are black, and polar bears are the only ones who can be other colors. So if you see a bear that's not black, you know it's a polar bear. But if you see a black bear, it could be a polar bear, or a grizzly bear, or any other kind of bear.

DaveE

[transgalactic]

thanks