Q252

[NatiO304]

I think the "neither/nor" is tripping me up here - can someone please explain?

Neither P nor Z will volunteer if K volunteers.

it must be true that...

-P --> K

P --> -K


-P --> K is the correct answer.

[ohthatpatrick]

"neither nor" means = "not this" AND "not that"

People often use the word "or", because it rhymes with "nor", but think about how neither/nor works:

If you are housesitting, you can neither set the bedroom on fire nor drink my $300 bottle of scotch.

We're prohibiting BOTH those actions.
HOUSITTING --> ~SET BEDROOM ON FIRE and ~DRINK EXPENSIVE SCOTCH

Neither P nor Z will volunteer if K volunteers.
K volunteers --> P will not and Z will not

K --> ~P and ~Z

You can split up "and" on the right side. Since both ~P and ~Z are guaranteed consequences of K, it's fair to say
K --> ~P
as well as
K --> ~Z

If we contrapose the original
K --> ~P and ~Z
we get
P or Z ---> ~K

You can split up "or" on the left side. Since P and Z are EACH capable of triggering ~K, it's fair to say
P --> ~K
Z --> ~K

hope this helps