I think you can conclude that:
1) B may not be infinite unless A is infinite
2) A may not be undefined.
3) If A is finite, B must be finite
----- Original Message -----
From: "John Hall" <firstname.lastname@example.org>
To: "Jeff Bone" <email@example.com>
Cc: "FoRK" <firstname.lastname@example.org>
Sent: Thursday, May 03, 2001 4:41 PM
Subject: RE: How do you teach fundamental logic to someone that doesn't grok
> It is the first one that shocks me. A => B, A, means B
> As to the second, you can conclude nothing. Specifically, you have no
> information about A.
> A => B, B, no extra conclusions can be drawn.
> I have run into people that confused A => B with A <=> B. I think is
> relatively common, if you teach it to a normal high school class.
> -----Original Message-----
> From: Jeff Bone [mailto:email@example.com]
> Sent: Thursday, May 03, 2001 4:04 PM
> To: John Hall
> Cc: FoRK
> Subject: Re: How do you teach fundamental logic to someone that doesn't
> grok it?
> Not sure what you're getting at, John. In the second case, the only
> things you can conclude are trivial: B, A OR B, etc... so what's
> your point? Is it just that: the only things you can conclude in the
> second case are trivial statements from the givens? Why is that hard
> to understand? I guess I've never run into a person who can get the
> first example, but falls into the trap on the second. I'm sure they
> exist, though; nothing about people's reasoning skills or lack
> thereof shocks me anymore.
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