neither nor

hihihi9993

If, "neither P nor K are cute", then can you say P+K→/C or do you have to keep them separate??

Lawgical Translations:
P → /C
AND
K → /C

Therefore, P+K→/C ?

Thank you!!!!

hihihi9993

Also what if "Jane will select neither the blue nor the black dress: Jane will not select Blue dress AND Black dress"??

Can you sum them up as J→/Blue + /Black?
or do you have to separate them as J→/Blue AND J→/Black?

@..@!!

So confusing.

Thank you in advance!!!

TheLSAT

The entities should remain separate for the following reason: P+K ----> /C indicates that they are not cute when combined. But the original statement said that neither P nor K are cute, which means each entity on its own is not cute. In your example, the sentence became as the following: if P and K, then not cute. I hope this makes sense.
Same reasoning applies to your second scenario.

Freddy_D

I would translate the original like this:

P or K -----> C

then utilizing DeMorgan's Law for the contrapositive

C ------> P and K

the "neither nor" is essentially an "either or" statement with a negation applied to it

hihihi9993

@TheLSAT said:
The entities should remain separate for the following reason: P+K ----> /C indicates that they are not cute when combined. But the original statement said that neither P nor K are cute, which means each entity on its own is not cute. In your example, the sentence became as the following: if P and K, then not cute. I hope this makes sense.
Same reasoning applies to your second scenario.

@TheLSAT
I got the part that "and" cannot be established because "each entity on its own is not cute". Then what about "inclusive or"?

@Freddy_D said:
I would translate the original like this:

P or K -----> C

then utilizing DeMorgan's Law for the contrapositive

C ------> P and K

the "neither nor" is essentially an "either or" statement with a negation applied to it

@Freddy_D
I have a sense that "'neither nor' is essentially an 'either or' statement with a negation applied to it", but I keep getting P/K → /C (Contrapositive: C → /P and /K) when I try drawing out the process.

I will try to show my thoughts as clearly as possible!!! Plz help!!

According to the video lecture, "neither" means "not one and not the other". So if we have "Neither P nor K are C", then it would be "P are not C AND K are not C".

P→/C AND K→/C:
When []? Then []
P? /C
K? /C
P, K? /C
P, /K? /C
/P, K? /C
/P, /K? Unknown
C? /P and /K

Then I tried to condense P→/C AND K→/C to something simpler by using "And" and "Or".

P+K→/C (using and)
P? Unknown
K? Unknown
THEREFORE, =/= to the original statement

P/K→/C (using inclusive or)
P? /C
K? /C
P, K? /C
P, /K? /C
/P, K? /C
/P, /K? Unknown
C? /P and /K
THEREFORE, = to the original statement

Thank you both @TheLSAT and @Freddy_D !!!

akistotle

@d931n027h said:
If, "neither P nor K are cute", then can you say P+K→/C or do you have to keep them separate??

This would be separate because it means that "P are not cute" and "K are not cure" separately.
P → not cute
K → not cute

P
or → /C
K

P↘︎
　　/C
K↗︎

https://7sage.com/lesson/neither-nor/

@Freddy_D said:
I would translate the original like this:

P or K -----> C

This translation would be "If it is not P or not K, then it is cute" ("Non-P or Non-K are cute").

Freddy_D

Lol I just realized that after the fact. Thanks, @akistotle

akistotle

@d931n027h said:
Also what if "Jane will select neither the blue nor the black dress: Jane will not select Blue dress AND Black dress"??

Can you sum them up as J→/Blue + /Black?
or do you have to separate them as J→/Blue AND J→/Black?

This basically means that "Jane won't select the blue dress" and "Jane won't select the black dress."

Jane select→/Blue dress
Jane select→/Black dress

=
　　　　　　/Blue dress
　　　　↗︎
Jane select
　　　　↘︎
　　　　　/Black dress

---

Blue dress→/(Jane select)
Black dress→/(Jane select)

=

Blue dress
　　　　↘︎
　　　　　/(Jane select)
　　　　↗︎
Black dress

akistotle

@Freddy_D said:
Lol I just realized that after the fact. Thanks, @akistotle

No problem

@d931n027h said:
I have a sense that "'neither nor' is essentially an 'either or' statement with a negation applied to it", but I keep getting P/K → /C (Contrapositive: C → /P and /K) when I try drawing out the process.

Yes, you are right.

P
or → /C
K

It really is simple: Neither nor = Not one and not the other.
https://7sage.com/lesson/neither-nor/

TheLSAT

@d931n027h Can you elaborate on your question because your original statement did not have an inclusive or. Neither P nor K are cute translates as the following in English: P is not cute And K is not cute. Maybe I'm missing something, so tell me more.

TheLSAT

If I was to encounter such a statement on a test, I would just keep them separate without the "or". That's just my personal preference though. So I'd just write the following:
P ----> /C
K ---> /C.
However, If P or K, then /C would also do the trick. So it's up to you to choose how to diagram them. Just make sure you do not put an "AND" in the sufficient condition.

hihihi9993

Thank you @Freddy_D @akistotle @TheLSAT

@TheLSAT said:
@d931n027h Can you elaborate on your question because your original statement did not have an inclusive or. Neither P nor K are cute translates as the following in English: P is not cute And K is not cute. Maybe I'm missing something, so tell me more.

I didn't explicitly say "inclusive or" in my original statement because I didn't know it could act as same as "neither nor"! I agree with you that I shouldn't put "and" as a replacement. However, it's okay to put "and or = inclusive or" in a replacement for "neither nor" because they are essentially same thing if you see my diagram!

@d931n027h said:
According to the video lecture, "neither" means "not one and not the other". So if we have "Neither P nor K are C", then it would be "P are not C AND K are not C".

P→/C AND K→/C:
When []? Then []
P? /C
K? /C
P, K? /C
P, /K? /C
/P, K? /C
/P, /K? Unknown
C? /P and /K

Then I tried to condense P→/C AND K→/C to something simpler by using "And" and "Or".

P+K→/C (using and)
P? Unknown
K? Unknown
THEREFORE, =/= to the original statement

P/K→/C (using inclusive or)
P? /C
K? /C
P, K? /C
P, /K? /C
/P, K? /C
/P, /K? Unknown
C? /P and /K
THEREFORE, = to the original statement