Plane Crash Survival: At Most One of Them

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SUMMARY

The discussion centers on the logical expression representing the statement "at most one of them will survive the plane crash," specifically involving three individuals: Albert, Bill, and Cory. The correct logical formulation is expressed as ¬[(A ∧ B) ∨ (B ∧ C) ∨ (C ∧ A)], where ¬ denotes negation, ∧ represents logical AND, and ∨ signifies logical OR. Participants confirm that this expression accurately captures the scenarios where either zero or one individual survives, while being false if two or three survive.

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Homework Statement


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".

Homework Equations


The Attempt at a Solution


[tex] \sim[(A\&B)\vee((B\&C)\vee(C\&A))][/tex]

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

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