this post was submitted on 17 Jan 2024
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No Stupid Questions

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[–] Boinkage@lemmy.world 95 points 9 months ago (6 children)

No. It is equal to "if not B, then not A." You're welcome for doing your logic 101 homework for you.

[–] pineapplelover@lemm.ee 31 points 9 months ago

First thing I thought lmao. Somebody is taking logic

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[–] Ragdoll_X@lemmy.world 42 points 9 months ago* (last edited 9 months ago)

An example of why this is incorrrect.

If a card is the ace of spades, it is black.

A card is black if and only if it is the ace of spades.

There are other conditions under which B (a card is black) can happen, so the second statement is not true.

A conclusion that would be correct is "If a card is not black, it is not the ace of spades.". The condition is that if A is true B will also always be true, so if B is false we can be sure that A is false as well - i.e. "If not B, not A".

[–] Ep1cFac3pa1m@lemmy.world 20 points 9 months ago* (last edited 9 months ago) (2 children)

If Nazi, then fascist = true

Fascist, if and only Nazi = not true

If car, then vehicle = true

Vehicle if and only if car = not true

[–] Valmond@lemmy.mindoki.com 4 points 9 months ago (1 children)

I used the bananas are fruits analog but your one works well too!

[–] Ep1cFac3pa1m@lemmy.world 7 points 9 months ago (1 children)

I just figured with Lemmy’s interest in politics it seemed like an obvious example. I threw in the car because I didn’t want to be that guy who makes everything about nazis…

[–] Boinkage@lemmy.world 3 points 9 months ago (1 children)

Yeah careful with that, the logic example Nazis will be all over you if you don't mix it up some.

[–] Ep1cFac3pa1m@lemmy.world 5 points 9 months ago

Not everything is about Nazis, Boinkage, geez…

[–] Lafari@lemmy.world 1 points 9 months ago (3 children)

If car, then vehicle = true

Car if and only if vehicle = true.

Is this correct?

Therefore "If A then B" = "A if and only if B" (or "If B then A" = "B if and only if A")?

[–] zenharbinger@lemmy.world 6 points 9 months ago* (last edited 9 months ago)

B can still be true when a is false. iff means that b can only be true when a is true.

Also, the equivalent statement is.

vehicle if and only if car.

not

car only if vehicle

since a truck is a vehicle, the statement is false.

Somewhat wrong above:

A B a iff b

T T T

T F F

F T F

F F T

look online for truth tables.

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[–] Maddie@sh.itjust.works 16 points 9 months ago (17 children)
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[–] feedum_sneedson@lemmy.world 13 points 9 months ago
[–] Apepollo11@lemmy.world 12 points 9 months ago

You've have some examples, but in case they are not clear enough:

If [you have AIDS] then [you are unwell]

[You are unwell] if and only if [you have AIDS]

The first one is not the same as the second. Why? There are plenty of ways to be unwell, without necessary developing AIDS.

The first statement only defines one possible path to B, not all of them.

[–] Some_Dumb_Goat@pawb.social 12 points 9 months ago

If A, then B

If Not B, then Not A

If it's raining then the grass is wet, but you can't tell if it's raining if the grass is wet, because of say, a hose or sprinkler.

All that you can tell is that if the grass is dry, then it is not raining, and I that's called a contrapositive.

[–] flx@lemmy.blahaj.zone 8 points 9 months ago

if youre doing homework, i recommend writing out truth tables for the statements and comparing, gives you a bit more insight into the statement truth conditions

[–] Neon@lemmy.world 7 points 9 months ago* (last edited 9 months ago) (1 children)

if I brake, my Car will stop.

will my Car only stop if i brake?

[–] lrnz92@feddit.it 3 points 9 months ago (1 children)
[–] Neon@lemmy.world 4 points 9 months ago

shhhhhhh. Nobody saw, nobody knows.

Also It's 00:30 over here, cut me some Slack.

[–] Moobythegoldensock@lemm.ee 7 points 9 months ago* (last edited 9 months ago) (1 children)

“If X is cat, then X is mammal” =?> “X is mammal if and only if X is cat”

Obviously doesn’t hold: What if X doge?

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[–] Kolanaki@yiffit.net 5 points 9 months ago (2 children)

I just saw a video on all the logical fallacies that exist, and this was one of them but my shit-ass memory can't recall what the name of the fallacy was.

[–] Lafari@lemmy.world 2 points 9 months ago

I think it's affirming the consequent

[–] rufus@discuss.tchncs.de 4 points 9 months ago* (last edited 9 months ago)

A => B is not the same as B <=> A

[–] jbrains@sh.itjust.works 3 points 9 months ago* (last edited 9 months ago) (1 children)

No.

B iff A is defined as "If B then A and if A then B".

If that doesn't make it clear enough for you, then try writing out the truth table for both statements.

[–] Lafari@lemmy.world 1 points 9 months ago (2 children)

I think I understand now, but what has left me scratching my nose (metaphorically):

Why is it called "B if and only if A", if what it really means is "B only if A and vice versa"? (Am I correct in thinking that's what it means?)

I just don't understand how that translates grammatically. To me, "B if and only if A" sounds the same as "B only if A". I can accept that they mean different things in the context of logic, just like I can assign any meaning to any label, like I could say that "dog" now means "kite" in a certain context. But it seems unintuitive and doesn't really make sense to me. Does that make sense?

[–] jbrains@sh.itjust.works 2 points 9 months ago* (last edited 9 months ago)

"B if and only if A" is a shorthand way to write "B if A and B only if A". It's like how "He is young and thin" means "He is young and he is thin". We could write it the second way without trouble, but the first way is shorter, we agree that they mean the same thing, and we prefer to conserve energy when writing.

The form "if and only if" is merely a convenient shorthand. Shorthand is usually more convenient for the writer than for the reader. 🤷‍♂️

Imagine these natural language sentences and analyze how they are different:

  • I'll go outside if it's not snowing
  • I'll go outside only if it's not snowing

Hint: what do you do in each case when it's snowing?

[–] ook_the_librarian@lemmy.world 1 points 9 months ago* (last edited 9 months ago)

"If A then B" means if A is true, then B is guaranteed to be true. Note that if B is true and A is false, "if A then B" is still true.

"B only if A" means the only way for B to be true is for A to be true. It's weird, but it has the inverse truth table as "(not A) and B".

[–] krdo@lmmy.net 1 points 9 months ago

The first statement only tells you when B is true. It says nothing about when it is false. The second statement both tells you when B is true (if A) and when it is not (only if A). Therefore, the two statements cannot be equal.

[–] Toes@ani.social 1 points 9 months ago* (last edited 9 months ago)
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