I'm looking at a worksheet that expresses boolean logic expressions using multiplication, addition, and apostrophes; something I've never seen before.

I can make a guess that the apostrophe is equivalent to ¬ (except it's suffixed instead of prefixed). But I'm not sure what the addition and multiplication of the variables/propositional atoms would mean. Furthermore, I don't know how a boolean logic formula can "output" something other than just a truth value...

I can't seem to piece together with certainty the meaning of this representation. Could anyone take a look at the below example and maybe make a guess as to a translation of this representation to the more traditional ^, v, and ¬ symbols?

This arose in the context of digital logic in terms of logic gates and such on a CPU, if that makes a difference.

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An alleged truth table of the above two expressions (the first row is filled in as an example):

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  • $\begingroup$ @ShyPerson Thank you very much! I guessed that but didn't think it worked, but looking back now it would make sense! Do you know why they have a specific term written in the box? Is that just the term in the expression that turns out to be true, do you think? $\endgroup$ – James Ronald Nov 4 '19 at 12:52
  • $\begingroup$ @JamesRonald: Yes, it looks like that's the term that makes the whole expression true. $\endgroup$ – ShyPerson Nov 4 '19 at 19:16
  • $\begingroup$ @YuvalFilmus: Thanks for the encouragement to create an answer. I guess I'm still unsure about when to create a comment versus an answer. Is there some documentation somewhere that would clarify this? Many thanks $\endgroup$ – ShyPerson Nov 4 '19 at 19:17
  • $\begingroup$ @ShyPerson Generally speaking, it’s better for questions to have an answer. $\endgroup$ – Yuval Filmus Nov 4 '19 at 19:18
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    $\begingroup$ Do not post pictures of formulas, please. You can use LaTeX to type them, it's a lot more polite and generally friendlier. $\endgroup$ – Andrej Bauer Nov 4 '19 at 19:25

Usually $+$ means $\lor$, "multiplication" means $\land$, and $'$ means $\lnot$.

  • $\begingroup$ Thank you very much for the help! $\endgroup$ – James Ronald Nov 5 '19 at 17:15
  • $\begingroup$ Sure! Happy to. $\endgroup$ – ShyPerson Nov 5 '19 at 21:29

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