# Logic question

**URL:** <https://boards.straightdope.com/t/logic-question/818057>\
**Category:** Factual Questions\
**Created:** [July 17, 2018, 2:32am UTC](https://boards.straightdope.com/t/logic-question/818057 "2018-07-17T02:32:29Z")\
**Posts on this page:** 1\
**Showing post:** 21

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**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\
**Post date:** [July 17, 2018, 3:11pm UTC](https://boards.straightdope.com/t/logic-question/818057/21 "2018-07-17T15:11:39Z")

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> [@septimus](#):
>
> I think the actual definition of logic implication is used routinely by mathematicians reading or writing math, even math unrelated to logic puzzles.

I just saw an example of a logical conditional in [another current thread](https://boards.straightdope.com/sdmb/showthread.php?t=858860).

> [@Moral hypothetical: the dark knight](https://boards.straightdope.com/t/moral-hypothetical-the-dark-knight/818075/1):
>
> Joker appears in Gotham. He says “batman: if you don’t reveal your identity, I will kill people”. Batman doesn’t reveal his identity, joker kills people.

> [@Moral hypothetical: the dark knight](https://boards.straightdope.com/t/moral-hypothetical-the-dark-knight/818075/6):
>
> Of course, this example is somewhat muddied by the established and predictable pattern.
> 
> - Batman refuses to reveal his identity. Joker kills people.
> - Batman reveals his identity. Joker kills people.
> - Batman patrols Gotham City even more thoroughly than usual searching for the Joker. Joker kills people.
> - Batman runs off to the ass end of nowhere searching for Ra’s al Ghul or somebody. Joker kills people.
> - Batman adds nipples to his Batsuit. Joker kills people.
> - etc

The Joker wasn’t lying; he just conveniently neglected to mention what he would do if Batman did reveal his identity. The only way “if you don’t reveal your identity, I will kill people” would logically be considered a false statement is if Batman didn’t reveal his identity and the Joker didn’t kill people.  
This is something that inexperienced math students have to be taught to be careful about: just because a theorem is true doesn’t mean that its converse (or inverse) is true.

Mathematical theorems often have the form of conditional statements: “If A then B.” For a simple example: “If a (whole) number ends in a 5 then it is divisible by 5.” This is a true statement, because it’s possible for A to be true and B to be true (e.g. 35); it’s possible for A to be false and B to be false (e.g. 27); and it’s possible for A to be false and B to be true (e.g. 10). It just isn’t possible for A to be true and B to be false.

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