# Homework Help: Logic question

1. Jul 12, 2010

### iamsmooth

1. The problem statement, all variables and given/known data
A: Albert survived the plane crash
B: Bill survived the plane crash
C: Cory survived the plane crash

Create the sentence (sentential logic) "at most one of them will survive the plane crash".

2. Relevant equations

3. The attempt at a solution
$$\sim[(A\&B)\vee((B\&C)\vee(C\&A))]$$

(In case people use a slightly different notation: ~ = 'negation', v = 'or', & = and)

I think this covers all the cases where they do have two or three survivors. Can anyone see anything wrong with my logic?

Thanks!

2. Jul 12, 2010

### Dick

I don't see anything wrong with that. If 0 or 1 survive, it's true, if two or three survive it's false.