Prepare for the LSAT or discuss it with others in this forum.
sighsigh

Posts: 263
Joined: Wed Oct 20, 2010 8:47 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.

JamMasterJ

Posts: 6657
Joined: Sat Jan 29, 2011 7:17 pm

### Re: Quick question about 'unless'

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

Balthy

Posts: 665
Joined: Sat Apr 03, 2010 12:28 pm

### Re: Quick question about 'unless'

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).