Conditional statements that use "unless"

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DSman
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Conditional statements that use "unless"

Postby DSman » Wed Aug 22, 2012 8:33 pm

For some reason I always have to stop and think about these types of conditional statements which just wastes time on LG so I want to write down a bunch and please correct me.

1. "A is 2nd unless B is 3rd" This would be:

If B is 3rd then A is not second OR
If A is 2nd then B is not 3rd

2. "A is not 2nd unless B is 3rd"

If A is 2nd then B is 3rd
If B is not 3rd then A is not 2nd

3. A comes before B unless E is before F

IF E is before F then A is after B
If A is before B then E is after F

4. A cannot be before B unless E is before F

If A is before B then E is before F
If E is after F then A is after B

Do i have these down correctly? Thanks.

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relevantfactor
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Re: Conditional statements that use "unless"

Postby relevantfactor » Wed Aug 22, 2012 10:37 pm

DSman wrote:For some reason I always have to stop and think about these types of conditional statements which just wastes time on LG so I want to write down a bunch and please correct me.

1. "A is 2nd unless B is 3rd" This would be:

~A2->b3
~B3->2A


2. "A is not 2nd unless B is 3rd"

A2->B3
~B3->~A2


3. A comes before B unless E is before F

~A>B-->E>F
~E>F-->A>B



4. A cannot be before B unless E is before F
A>B-->E>F
~E>F-->~A>B



Do i have these down correctly? Thanks.

Unless is necessary even for games, so you cant flip the two, unless you use the contra-positive(in all statements). Also since unless will be the necessary, the sufficient would be negated. Just look at the examples.
And what you wrote seems to be correct, but I just skimmed :oops:
Does that help?

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Cerebro
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Joined: Thu Aug 09, 2012 9:22 pm

Re: Conditional statements that use "unless"

Postby Cerebro » Thu Aug 23, 2012 1:38 am

relevantfactor wrote:Unless is necessary even for games, so you cant flip the two, unless you use the contra-positive(in all statements).


I see what you did there.

Joeshan520
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Re: Conditional statements that use "unless"

Postby Joeshan520 » Thu Aug 23, 2012 1:52 am

The logic equivalent for unless is "if not" to indicate sufficiency.

Unless my shoes are tied, I will fall OR I will fall unless my shoes are tied

~ST -> F

Contrapositive

~F -> ST

Multiple ways to skin a cat

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relevantfactor
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Re: Conditional statements that use "unless"

Postby relevantfactor » Thu Aug 23, 2012 2:13 am

Cerebro wrote:
relevantfactor wrote:Unless is necessary even for games, so you cant flip the two, unless you use the contra-positive(in all statements).


I see what you did there.


Lol :lol:

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PDaddy
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Re: Conditional statements that use "unless"

Postby PDaddy » Thu Aug 23, 2012 3:34 am

Unless I am Handsome, I will be Unhappy.

H --> U

U --> H

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Lyov Myshkin
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Re: Conditional statements that use "unless"

Postby Lyov Myshkin » Thu Aug 23, 2012 5:01 am

it doesn't rain unless there are clouds.

always have a good example memorized rather than the formula since you could easily incorrectly remember a formula which doesn't already intuitively feel true to you, but it's pretty hard incorrectly reason what this 'unless' conditional must be (in terms of arrows and letters and such) from a good example.

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DSman
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Re: Conditional statements that use "unless"

Postby DSman » Thu Aug 23, 2012 6:07 am

relevantfactor wrote:
DSman wrote:For some reason I always have to stop and think about these types of conditional statements which just wastes time on LG so I want to write down a bunch and please correct me.

1. "A is 2nd unless B is 3rd" This would be:

~A2->b3
~B3->2A


2. "A is not 2nd unless B is 3rd"

A2->B3
~B3->~A2


3. A comes before B unless E is before F

~A>B-->E>F
~E>F-->A>B



4. A cannot be before B unless E is before F
A>B-->E>F
~E>F-->~A>B



Do i have these down correctly? Thanks.

Unless is necessary even for games, so you cant flip the two, unless you use the contra-positive(in all statements). Also since unless will be the necessary, the sufficient would be negated. Just look at the examples.
And what you wrote seems to be correct, but I just skimmed :oops:
Does that help?


Thanks for the response but I'm confused about this one:

"A is 2nd unless B is 3rd" This would be:

~A2->b3
~B3->2A


Shouldn't this be

B3 -> ~A2
A2 -> ~B3

What you wrote and what I wrote both make sense to me. If B is 3rd, then A cannot be second. You wrote it a different way. you said that a is not second if B is third. Don't both of these make sense? Im confused.

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Ixiion
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Re: Conditional statements that use "unless"

Postby Ixiion » Thu Aug 23, 2012 6:53 am

DSman wrote:Thanks for the response but I'm confused about this one:

"A is 2nd unless B is 3rd" This would be:

~A2->b3
~B3->2A


Shouldn't this be

B3 -> ~A2
A2 -> ~B3

What you wrote and what I wrote both make sense to me. If B is 3rd, then A cannot be second. You wrote it a different way. you said that a is not second if B is third. Don't both of these make sense? Im confused.


No, because you wrote
B3 -> ~A2
Which means If B is 3rd, A is not 2nd. That's true, but that's also giving way to the possibility that A is not 2nd even if B is not 3rd. So, in your equation, you could mistakenly draw your diagram this way:
(B1) 2 3 (A4) and it would still follow that rule, but it would be incorrect.

A2 -> ~B3
Again, still correct, but even with BOTH of your rules here, none of them say that A MUST be 2nd, which is what the original rule said. So you could make a lot of mistakes this way.

The way relevantfactor wrote it:
~B3 -> A2
says that if B is not 3rd, A is 2nd. Which is more encompassing and says that A must be 2nd if B is not 3rd.

and ~A2 -> B3
if A is not 2nd, B must be 3rd, because otherwise A is always 2nd, and so there's only one time when A is not 2nd, and that is when B is third. That's better understood when you see ~B3 -> A2 first.

Does that make sense?

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banjo
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Re: Conditional statements that use "unless"

Postby banjo » Thu Aug 23, 2012 11:19 am

Joeshan520 wrote:The logic equivalent for unless is "if not" to indicate sufficiency.


This is the best way to think about it. No matter where it appears in a conditional sentence, unless = if..not. If you've taken any Latin, think of how you'd translate nisi.

Techsan23
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Joined: Wed Jul 20, 2011 10:21 pm

Re: Conditional statements that use "unless"

Postby Techsan23 » Thu Aug 23, 2012 11:43 am

Just memorize "negate sufficient". Whatever you negate becomes sufficient.

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DSman
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Joined: Wed Jun 27, 2012 4:27 am

Re: Conditional statements that use "unless"

Postby DSman » Thu Aug 23, 2012 4:20 pm

Ixiion wrote:
DSman wrote:Thanks for the response but I'm confused about this one:

"A is 2nd unless B is 3rd" This would be:

~A2->b3
~B3->2A


Shouldn't this be

B3 -> ~A2
A2 -> ~B3

What you wrote and what I wrote both make sense to me. If B is 3rd, then A cannot be second. You wrote it a different way. you said that a is not second if B is third. Don't both of these make sense? Im confused.


No, because you wrote
B3 -> ~A2
Which means If B is 3rd, A is not 2nd. That's true, but that's also giving way to the possibility that A is not 2nd even if B is not 3rd. So, in your equation, you could mistakenly draw your diagram this way:
(B1) 2 3 (A4) and it would still follow that rule, but it would be incorrect.

A2 -> ~B3
Again, still correct, but even with BOTH of your rules here, none of them say that A MUST be 2nd, which is what the original rule said. So you could make a lot of mistakes this way.

The way relevantfactor wrote it:
~B3 -> A2
says that if B is not 3rd, A is 2nd. Which is more encompassing and says that A must be 2nd if B is not 3rd.

and ~A2 -> B3
if A is not 2nd, B must be 3rd, because otherwise A is always 2nd, and so there's only one time when A is not 2nd, and that is when B is third. That's better understood when you see ~B3 -> A2 first.

Does that make sense?


Yep that clears it. Thanks for the help.




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