# Questions tagged [boolean-algebra]

Boolean algebras are structures which behave similar to a power set with complement, intersection and union. Use this tag for questions about Boolean algebras as structures, or about functions defined from/to Boolean algebras. For Boolean logic use the tag propositional-calculus.

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### Does the variety of Boolean Algebras contain no proper nontrivial subvarieties/subquasivarieties?

Consider the variety, in the sense of universal algebra, of Boolean Algebras in the language $\{\cup,\cap,',0,1\}$, where $'$ represents complementation, and the other symbols are well known. I ...
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### How to find the minimum sum of products expression from a two variable truth table with only one 0?

I am looking for a minimum sum of products expression from this truth table: A B f 0 0 1 1 0 0 1 1 1 0 1 1 From my understanding, I can create the minimum sum of products expression from the ...
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### I dont understand how to solve this Boolean Algebra question Help

Let S be a set and let F UN(S, {0, 1}) be the set of all functions with domain S and codomain {0, 1}. Define the Boolean operations on F UN(S, {0, 1}) as follows: Let F, G ∈ F UN(S, {0, 1}), then (a) ...
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### How Do I simplify This Boolean Expression? [duplicate]

Expression: $$XY' + Y'Z' + X'Z'.$$ I think it has something to do with the consensus formula, but I can't actually figure out how to approach this problem.
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### Inverse of a boolean lower unitriangular matrix

Is the inverse of a boolean lower unitriangular matrix identical to the matrix itself? The matrix entries are considered to be in GF(2), i.e. bool.
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### Boolean NOT is missing: the count of items in set A but not in set B is the count of items in either set less the count of items in B, right?

A computer system I'm accessing has a weird query limitation: I can query using AND and OR Boolean operators, but NOT is restricted. However, there's a way around this limitation, isn't there? I've ...
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1 vote
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### Simplification of boolean expression algorithms allowing multiple input gates

I am looking to algorithmically generate simplified diagrams of boolean logic that exists in a DCS program. I have come across a number of online boolean expression simplification tools, that use De ...
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### Finite Commutative ring with 100 elements where $x^2=x$?

Does there exist a finite Commutative ring with 100 elements where $x^2=x$ for every $x\in R$? I know finite Boolean rings has the property this property but they have cardinality $2^n$, for some $n$. ...
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### Gray code permutation notation

I 'm trying to understand the notation of the Gray code permutation but since I only know 2-row matrix notation for permutations, I would like an explanation for the notations below . I understand the ...
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### A statement that seems to be neither true nor false [closed]

Let us consider a statement A that says "Statement A is false". Now is the statement A true or false? If it's false then statement that says "Statement A is false" is true ...
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### A generalized algorithm to convert a formula in algebraic normal form to an equivalent formula that minimizes the number of bitwise operations

In this question, “bitwise operation” means any operation from the set {XOR, AND, OR}. The NOT operation is not included because ...
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### Quantifier elimination for Boolean algebras

Is there a reference in English for the proof that Boolean algebras admit quantifier elimination? I'm interested in how quantifier elimination can be performed. However, the result of Tarski is not ...
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### Why can a compound biconditional statement whose individual statements don't all have the same truth values be true?

Why can $P_1 ⇔ P_2 ⇔ P_3 ⇔ \ldots ⇔ P_n$ be true when not all the $P$’s have the same truth value? For example: If P1 = T P2 = T P3 = F P4 = F would this be true? T(P1) ⇔ T(P2) ⇔ F(P3) ⇔ F(P4) = ...
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