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Three friends enter a shoe shop and approach the seller. The seller asks them; will all 3 of you buy shoes?

The answers are as follows:

A: I don't know

B: I don't know

C: No

Which guy/guys will buy shoe/shoes?

What I think:

I think that the first two guys will buy shoes. Since they don't answer no to the question means that they are going to buy shoes but they don't know what the others will do otherwise they could have just said 'No'right away. My problem is that I don't know how to express that with math and logic operators like '∧','¬','∨' e.t.c.

We're All Mad Here
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    What is it, exactly, that you want to describe using statements and logical operators? –  Mar 01 '16 at 19:18
  • If what I think is correct then my process of thinking. The way I described it with words but using statements, operators, truth tables whatever is simpler if possible. – We're All Mad Here Mar 01 '16 at 19:20
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    Your thinking is absolutely correct, but what does the translation into a formula improve ? The solution with words will probably be far easier to understand. – Peter Mar 01 '16 at 19:23
  • Yes, but I was thinking perhaps it may not be solid enough :p – We're All Mad Here Mar 01 '16 at 19:24
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    The situation is clear : If you buy a shoe, than you cannot know, whether all buy shows without knowing what the others do. If you do not buy a shoe, you can be sure that not all buy shoes. – Peter Mar 01 '16 at 19:26
  • Thank you I think you are right, I will just give the solution with words, but since the provided answer is correct as well I'll accept it, thank you for your time! – We're All Mad Here Mar 01 '16 at 19:28

1 Answers1

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Let $F_i$ denote whether the $i^{th}$ friend buy shoes (i.e., if $F_i$ is true, the $i^{th}$ friend will buy shoes).

Now the vendor asks "$F_1 \wedge F_2 \wedge F_3$?". If $F_1$ was false, then the first friend could reply $F_1 \wedge F_2 \wedge F_3$ is false. Since he doesn't, it means that $F_1$ is true. Same goes with $F_2$. Now comes $F_3$ who replies $F_1 \wedge F_2 \wedge F_3$ is false. Since we know both $F_1$ and $F_2$ to be true, $F_3$ must be false.

We conclude that the two first friends will buy shoes, but not the third one.

TheNicanova
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