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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.

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.

A Boolean algebra uses Boolean variables, typically denoted by capital letters, e.g. $A,B$, which can only take the values $0$ or $1$. Operators are $\land$ (conjunction), $\lor$ (disjunction) and $\lnot$ (negation).

For Boolean logic use the tag .

3083 questions
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Simplification of: AB + A'C + BC in boolean algebra

I am trying to understand the simplification of the boolean expression: AB + A'C + BC I know it simplifies to A'C + BC And I understand why, but I cannot figure out how to perform the simplification through the expression using the boolean algebra…
M. S.
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Cardinality of Boolean algebras generated by partitions and some eextra elements.

Consider a parttion of the unity of a finite Boolean algebra and two different elements of the algebra. What is the cardinality of the algebra generated by the union of the partition and the set consisted of the two elements? Extend the problem to…
val 72
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Simplifying Boolean functions

How do I simplify the Boolean function: ABC + B I've tried doing De Morgan's, but that doesn't do anything to simplify this. Can somebody show the steps on how to simplify this please?
joe
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What is the easiest way to find $K$ when $A$ $XOR$ $K$ is given and A is unknown?

A $XOR$ $K$ is given. Both $A$ and $K$ are unknowns. Can the value of $K$ be guessed? Can the values of $K$ can be deduced if the size of $A$ & $K$ are known? What is the smallest set on which bruteforcing can be performed to get the value of…
hax
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Boolean Algebra simplification - odd number terms

I'm new to boolean algebra and having problems simplifying expressions with odd number terms, Expressions such as: 1. A'B'C'D + A'B'CD + AB'C'D + AB'CD + ABC'D 2. A'BC + AB'C' + A'B'C' + AB'C + ABC Here is my logic for both…
joao
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Monomorphism between finite Boolean algebras

Let $A$ be a finite Boolean algebra. If I define a monomorphism (i.e. an injective homomorphism) from $A$ to another finite Boolean algebra $B$ of the same similarity type. Is this monomorphism an isomorphism? I am tempted to think that yes, for two…
user60264
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Isolate $A$ from $A\oplus(129^3A)$

I've been working through the following problem and I'm really stuck Starting with the following three equations: $$ a= (129A \oplus C)\mod 256 \\ b= (129B \oplus A) \mod 256\\ c= (129C \oplus B) \mod 256 $$ I xor'd both sides of the equation and…
ZnArK
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Having trouble with simplifying in Boolean algebra

I want to solve this problem: $$(x . y . z + x . y + x)$$ Which turns into this when you group $x$ $$x . ( yz + y + 1 ) $$ What I don't understand is why is there a "1" at the end? Does the last $x $ turn into a 1? If so, why? My math…
Sinan Samet
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boolean algebra reduction question

hi im having a lot of trouble proving this boolean expression. Im getting many differing answers so I assume I must be going about it in the wrong way. To explain, I'm trying to negate the whole LHS to split up the brackets and then trying to use…
dmnte
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General rules for transforming boolean equations?

Are there general or restricted rules for transforming between equivalent boolean equations? A concrete problem that I have is given the following equation: p -> (r <-> q) = True Is it possible to transform it to an equation with r on the left and…
Phil
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Can $P(\omega)$ be superatomic?

A Boolean algebra is superatomic if its every subalgebra has an atom. I'm trying to determine whether $P(\omega)$, i.e. the power set algebra of the set of all natural numbers (finite ordinals) $\omega$, can be superatomic. In the algebra…
Gur Ismael
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Tests for combinational logic - product of sums simplification

I am trying to understand how to simplify the Boolean cover function $(4+6)(12+14)(0+1+2+3)(11)(3)(9)(13)(10+14)(1+3+9)$ which is a stuck-at fault test cover function derived in this paper. I know the result should be $(3)(9)(11)(13)(4)(14)$ or…
Student
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Want to check if my Boolean Algebra simplification is correct

$(A+B)(B+\bar B)(\bar B+C)$ Distributive LAW $(AB+A \bar B+B B+B \bar B)(\bar B+C)$ Distributive LAW $(A B \bar B+A B C+A \bar B \bar B+A \bar B C+B B \bar B+B B C+B \bar B \bar B+B \bar B C)$ Idempotent Law {} + Complementary Law [] $(A [B \bar…
Mantra4321
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Boolean algebra - Maxterms

I have a boolean expression and I need to get to its canonical forms (sum of minterms and product of maxterms). In order to get an expression for the first canonical form, I need to multiply every term by $(x + x')$, where $x$ is the missing…
Vinícius Lopes Simões
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Boolean Algebra - Prove XYZ + XYZ' + XY'Z + X'YZ = XY + XZ + YZ

Trying to prove $((X\land Y\land Z)\lor (X\land Y\land \lnot Z)\lor (X\land \lnot Y\land Z ) \lor (\lnot X\land Y\land Z)) \equiv ((X\land Y)\lor (X\land Z)\lor (Y\land Z))$ and I am a bit stuck. I have the following: $\equiv X\land Y\land (Z\lor…
mercho
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