How do I turn this question into a boolean logic problem?

StackOverflow https://stackoverflow.com/questions/2286096

  •  21-09-2019
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Question

"If you can press a button to get $1M and a random person dies somewhere in the world would you press the button?"

A = press button

B = get $1M

C = random person dies

Here is what I think it should be:

If A, then B AND c

According to the original statement is it:

(If A, then B) AND C

or

If A, then (B AND C)
Was it helpful?

Solution

You've correctly identified the three propositional variables:

  • P1(x): "x presses a button."
  • P2(x): "x receives one million dollars."
  • P3(x): "x causes the death of a random person."

You want to express the sentence Q: "if someone presses the button, then they receive a million dollars and a person dies." At first glance, it seems like P1(x) ⇒ P2(x) ∧ P3(x) correctly expresses this. How can we be sure? Let's draw a truth table:

 P1   P2   P3   P2 ^ P3   P1 --> P2 ^ P3
---- ---- ---- --------- ----------------
 T    T    T       T            T
 T    T    F       F            F
 T    F    T       F            F
 T    F    F       F            F
 F    T    T       T            T
 F    T    F       F            T
 F    F    T       F            T
 F    F    F       F            T

Notice that "you receive a million dollars and cause a death" is true only when both of the constituent parts are true. This makes sense; if both parts don't come true, the whole is not also true.

Notice also the truth values for the entire statement Q: it's false whenever the second part is false and the first part is true. This makes sense: if you press the button but either (1) the million dollars doesn't appear or (2) nobody dies, the prediction implied by Q is not true. So our assertion is correct.

OTHER TIPS

Think about it. Draw up a truth table for each option.

HINT: If you don't push the button, would the random person die?

In all maths where the operators are the same and no logical grouping is indicated, the expression is read from left to right. Therefore, if you press the button, you will receive $1M and a random person will die.

I changed my mind. True. This is not programming. This is Ethical logic. Go to Community wiki.

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