Conditional statements that use "unless" Forum

[DSman]

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.

[relevantfactor]

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
Does that help?

[Cerebro]

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]

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

[relevantfactor]

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

[PDaddy]

Unless I am Handsome, I will be Unhappy.

H --> U

U --> H

[Lyov Myshkin]

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.

[DSman]

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
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.

[Ixiion]

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?

[banjo]

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]

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

[DSman]

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.