Getting Robbed Logically

Let's say you're delivering pizza in a shitty part of north Philly and this twitching guy with a tattoo on his chest tries to take your money. And let's say he's a better robber than he was in reality and he has a gun and says "Your money or your life." Let's explore, through symbolic logic, what you ought to do in this situation.

"Your money or your life," he says. Assuming the robber is not aversed to stealing from corpses, this statement can be broadened to mean "If not your money or your life, then your money AND your life."

If we take 'P' and 'Q' to stand respectively for 'your money' and for 'your life;' the symbol 'V' to stand for 'or' (more or less); the symbol '&' to stand for 'and' (more or less); the symbol '>' to stand for "if... then;" AND the symbol '-' to stand for 'not;' the symbolic rendering of this robber's threat is as follows:

-(P V Q) > (P & Q)

And if we take 'T' and 'F' to stand for 'True' and 'False,' this is the truth table for the threat:

P Q -(P V Q) > (P & Q)
T T F    T       T      T
T F F    T       T      F
F T F    T       T      F
F F T    F       F      F

The fifth column from the left (italicized) is that which speaks, logically, for the entire sentence -(P V Q) > (P & Q), and so we can see that the robber can end up with your money under these circumstances:

  1. You give him your money.
  2. You don't give him your money.

But look at the last row, which ends up as 'F.' In this circumstance he will take neither your life nor your money because, as a robber, he's some kinda puzzay. You can see there's a 25% chance of that. So, you know.

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