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I have four Boolean variables, , , and . The only thing that is known a priori about them is that . Now I want to do different things in my system depending on whether:
I needed to know that these three cases are mutually exclusive and that they cover all possibilities (or in other words, that exactly one of them is true, regardless of what "legal" values the variables have). Now, there are only sixteen possible values of the variables, only ten of which fulfil the requirement, so this is easily brute-forced either by hand or with a simple loop in any language. But as I'm curious, it would be satisfying to know how it could also have been solved algebraically (as I assume it could!), and I'm rusty and at a loss here. Any pointers on how to think would be appreciated. Jao ( talk) 11:43, 26 October 2022 (UTC)
Mathematics desk | ||
---|---|---|
< October 25 | << Sep | October | Nov >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
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The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I have four Boolean variables, , , and . The only thing that is known a priori about them is that . Now I want to do different things in my system depending on whether:
I needed to know that these three cases are mutually exclusive and that they cover all possibilities (or in other words, that exactly one of them is true, regardless of what "legal" values the variables have). Now, there are only sixteen possible values of the variables, only ten of which fulfil the requirement, so this is easily brute-forced either by hand or with a simple loop in any language. But as I'm curious, it would be satisfying to know how it could also have been solved algebraically (as I assume it could!), and I'm rusty and at a loss here. Any pointers on how to think would be appreciated. Jao ( talk) 11:43, 26 October 2022 (UTC)