Advanced Conditionals Lab

[LSAT-Chang]

Hello!
I just watched the advanced conditionals lab in the student center, and came across 2 phrases that I wasn't sure if we could split or not (I'm guessing this would be the right place to post this question)... So here goes:

1. Neither Sam nor Gerald will eat any cake that has no chocolate.

Can we have the following split:

~Chocolate -> ~SE
~Chocolate -> ~GE

and the contrapositives: SE -> Chocolate and GE -> Chocolate

the lab didn't mention anything about being able to split this or not so was wondering if it wasn't allowed.. I would assume so, since it is just saying that if there is no chocolate, then sam or/and gerald won't eat it. Right?

2. Both Lucy and Ricky must be home if Ethel is to be allowed in.

I guess we can't split this because it says "BOTH must be home and not just one" so if Ethel is allowed in, the both Lucy and Ricky must be home. Is this correct?

and the contrapositive would be: ~LH or ~RH --> ~EA

[chike_eze]

Hello!
2. Both Lucy and Ricky must be home if Ethel is to be allowed in.

I guess we can't split this because it says "BOTH must be home and not just one" so if Ethel is allowed in, the both Lucy and Ricky must be home. Is this correct?

and the contrapositive would be: ~LH or ~RH --> ~EA

I agree with your conditional statement, but I think it can be split.

Translation: LH and RH, if EA (same as if EA, then LH and RH)
i.e., EA --> LH and RH (contrapositive of your statement)

Therefore:

EA --> LH
EA --> RH
OR
~LH --> ~EA
~RH --> ~EA

Cheers.