Quick question about 'unless'

sighsigh
Posts: 263
Joined: Wed Oct 20, 2010 8:47 pm

Quick question about 'unless'

Postby sighsigh » Sat May 04, 2013 12:51 pm

I was always told we can express 'X unless Y' through formal notation as ~X => Y (or ~Y => X, the contrapositive).

But can't we also infer Y => ~X? Take this example:

This water is freshwater, unless it contains salt.
- If this water is not freshwater, then it contains salt.
- If this water does not contain salt, then it is freshwater. (contrapositive of above)

But, I'm pretty sure the following can also be inferred:
- If this water contains salt, then it is not freshwater.

Thanks guys.

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JamMasterJ
Posts: 6688
Joined: Sat Jan 29, 2011 7:17 pm

Re: Quick question about 'unless'

Postby JamMasterJ » Sat May 04, 2013 1:09 pm

sighsigh wrote:- If this water contains salt, then it is not freshwater.

Thanks guys.

no to this one, yes to the other two. That's an if and only if thing

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Balthy
Posts: 668
Joined: Sat Apr 03, 2010 12:28 pm

Re: Quick question about 'unless'

Postby Balthy » Sat May 04, 2013 1:56 pm

sighsigh wrote:I was always told we can express 'X unless Y' through formal notation as ~X => Y (or ~Y => X, the contrapositive).

But can't we also infer Y => ~X? Take this example:

This water is freshwater, unless it contains salt.
- If this water is not freshwater, then it contains salt.
- If this water does not contain salt, then it is freshwater. (contrapositive of above)

But, I'm pretty sure the following can also be inferred:
- If this water contains salt, then it is not freshwater.

Thanks guys.


Bob will fail this course unless he studies.

If Bob does not study, he will fail the course (like, seriously, for sure, cause it's a fucking hard course).
If he does not fail the course, you know that he studied (I'm tellin ya, you just can't get lucky in this course).


Now, you want to add:
If he studies, then Bob will not fail.

If you've taken any difficult courses, you know this last sentence is not necessarily true. There are courses where, if you don't study, you will certainly fail, but if you do study, you could still fail.




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