Conditional Reasoning Question from LSAT Interact

[hnadgauda]

While doing LSAT Interact, there is a quiz on diagramming the following statement: Neither S nor G will eat any cake that has no chocolate.

I don't understand how to diagram this properly. I (incorrectly) diagrammed it as follows: ~S-->~C; ~G-->~C

Can you please explain the reasoning behind the correct diagram?

[ohthatpatrick]

First of all, "Neither X nor Y" always means "Not X and not Y".

If I say, "Try this ice cream. It has neither poison nor broken shards of glass in it", then you are expecting the ice cream to have no poison AND no glass.

Secondly, the trigger word in the sentence you asked about is "any".

Neither S nor G will eat any cake that has no chocolate.

Conditional statements are about certainty, and certainty usually comes from
RULES (if, when, whenever)
UNIVERSALS (all, each, any, every, no, none)
GUARANTEES (ensures, leads to, inevitably results in)
REQUIREMENTS (requires, needs, must, depends on, only, only if, unless)

The sentence is saying,
For every non-chocolate cake in the universe, we can be certain that S and G won't eat it.

Equivalently,
S and G only eat chocolate cake.

We could say
"If it's a non-chocolate cake, then I am certain that S and G won't eat it."

Not-choc cake --> ~S and ~G

There is no guarantee that S and G will eat every single chocolate cake in the universe.

The way you symbolized it was
~S -> ~Choc Cake

which contraposes into
Choc cake --> S

S might politely refuse chocolate cake that has poison / glass in it.

[hnadgauda]

First of all, "Neither X nor Y" always means "Not X and not Y".

If I say, "Try this ice cream. It has neither poison nor broken shards of glass in it", then you are expecting the ice cream to have no poison AND no glass.

Secondly, the trigger word in the sentence you asked about is "any".

Neither S nor G will eat any cake that has no chocolate.

Conditional statements are about certainty, and certainty usually comes from
RULES (if, when, whenever)
UNIVERSALS (all, each, any, every, no, none)
GUARANTEES (ensures, leads to, inevitably results in)
REQUIREMENTS (requires, needs, must, depends on, only, only if, unless)

The sentence is saying,
For every non-chocolate cake in the universe, we can be certain that S and G won't eat it.

Equivalently,
S and G only eat chocolate cake.

We could say
"If it's a non-chocolate cake, then I am certain that S and G won't eat it."

Not-choc cake --> ~S and ~G

There is no guarantee that S and G will eat every single chocolate cake in the universe.

The way you symbolized it was
~S -> ~Choc Cake

which contraposes into
Choc cake --> S

S might politely refuse chocolate cake that has poison / glass in it.

Thanks for your response. I understand now that the statement is supposed to be diagrammed like the following:

~C-->~S
~C-->~G

I don't see how this is equivalent to S and G only eat chocolate cake because AND in the outcome translates to OR in the trigger. So the statement should be equivalent to If S or G is eating cake, the cake can only be chocolate cake.

Please let me know if I'm making a mistake.

[ohthatpatrick]

No, I was aware that was kinda confusing.

You're thinking a little too mechanically / literally. When we say "S and G only eat chocolate cake", that's not same as saying "If S happens and if G happens, then only eat chocolate cake".

If I say "Sarah and Greg are humans", we don't have to translate that into
"If someone is Sarah and Greg, they are human"
or
"If Sarah and Greg are both here together, then they are human"

You can think to yourself that "human" is a quality that is applicable to both Sarah and Greg.

If it's Sarah --> it's human, and she only eats choc cake
If it's Greg --> it's human, and he only eats choc cake

I haven't seen LSAT try to mess with us in that way, but this serves as a public service announcement that, as useful as memorizing conditional logic triggers is, we still need to engage our normal sense of reading comprehension and ask ourselves "Where is the certainty?"

If I'm dealing with S, am I certain that she will only eat choc cake?

According to the statement "S and G only eat choc cake", yes!