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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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Simplify this Boolean expression: $(BC'+A'D)(AB'+CD')$.

I need to simplify this Boolean expression: $(BC'+A'D)(AB'+CD')$ I'm unsure what the theorems say about this. But I've tried this, and not sure if this is the right way: $BC'AB' + BC'CD' + A'DAB' +A'DCD'$ ...and this is ezpz.
MZ97
  • 167
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Is $A\odot B\odot C = A\oplus B\oplus C$?

(The notations used: $\oplus$ is XOR operator $\odot$ is XNOR operator) I was solving a problem, where they asked which of the given options give equation for the difference of full subtractor. The circuit in the solution option was: For me the…
RajS
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Criterion for an Ideal in a Boolean algebra

"Joy of Sets" on p.26 states [as one criterion] that a non-empty set $I$ of a Boolean algebra $B$ is called an ideal if and only if: $b, c\in I\rightarrow b\vee c\in I$ If $b$ and $c$ are in $I$, how is it possible that $b\vee c$ not be an…
user12802
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Given a Boolean algebra $(B, \land, \lor)$ can I find a set $X$ such that $(B, \land, \lor) = (\mathcal{P}(X), \cap, \cup)$?

Suppose I have a set $B$ and operations $\land$ and $\lor$ and $\neg$ such that : $$ (B, \land, \lor, \neg) $$ is a Boolean algebra. Can I always find a set $X$ such that this Boolean algebra is isomorphic to the canonical Boolean algebra induced on…
Julien__
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When to Stop Simplifying a Well-Formed Formula?

I mean simplifying a wff(well-formed formula)in which, only $\lor$, $\land$, $()$and $\lnot$ are allowed, as minimizing the occurence of connective symbols( $\land$ and $\lor$). It's self-evident that there is no need to further simplifying wffs in…
Metta World Peace
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Solve Boolean system of equations

How can I solve a set of boolean equationst to get a,b,c and d. Like: w = a*b*c*d x = !a*b*d y = !b*a*d + !c*a*d + !a*b*c + !d*!a*b z = a*c w, x, y, z are known. This example above is very simple to solve via substituation. But what is with complex…
nt2005
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Is it possible, in Boolean Algebra, to add arbitrarily a new term to both sides of an expression?

First of all, i'm sorry for my english. I'll try to do my best to explain myself. I've been trying to look for it on the internet, but i'm not sure about the answer. I hope someone can help me here :) My question is: Is it possible to add a new term…
Federico
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Does a complete subalgebra A of a complete boolean B algebra always intersect all dense subsets of B?

I'm trying to show that if $(B, i)$ is the (BA) completion of any partial order $P$ and $A$ is a complete subalgebra of $B$, then $i^{-1}[A]$ is a complete suborder of $P$. Pure hunch says it's true, but i'm stuck at whether a complete subalgebra…
John Toh
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Is this the only solution to the problem?

Find all mutually non-equivalent $A(p,q)$ so that $(Aq\rightarrow \overline{p}) = (p+A)$ is true regardless of $p$ and $q$, where $\overline{x}$ is negation, $xy$ is conjunction, $x+y$ disjunction, $x\rightarrow y$ implication and $x=y$…
Luka Aleksić
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Simplification in a Boolean algebra

I tried to do question 7 of chapter 5-2 in Boolean Algebra and its Applications, by J. Eldon Whitesitt. Starting from table 5-1 and calling the function represented by the table $f$, I get \begin{equation} f = AB'C + AB'C' + ABC' +…
optical
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How to create AND with XOR and NOT

I can only create XOR and NOT gates, can I use them to create an AND gate? I was expecting this to be easy to find, but I was unable to do so. I´m quite unsure of what the answer might be, since unlike AND and OR gates, XOR has no output that is…
Freeman
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In Boolean Algebra what is the difference between AB vs A.B notations?

In Boolean algebra is AB the same as A.B and if not what are the differences between them? And going along those same lines is C(A+B) the same as C.(A+B)
Ninja2k
  • 195
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What are the names of these Boolean Algebraic Laws?

I need to simplify a Boolean algebraic equation and name the laws I use at each step, here is where I am at AB + AC + B I got the answer online but couldn't identity the law AB + AC + B (AB + B) + AC (Is this the commutative law?) B + AC (Name of…
Ninja2k
  • 195
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Mathematical description for boolean logic with "hysteresis" through logic-state dependence.

I am having trouble mathematically representing boolean logic gates that have logical hysteresis as they have "state". In asynchronous circuits for example, I have something similar to a AND gate called a Muller C-element that is very much like a…
b degnan
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How does A'BC' + AB'C' + ABC' simplify to (A + B)C'?

How does A'BC' + AB'C' + ABC' simplify to (A + B)C'? At least that's what I think the notation commonly used here seems to indicate, but I'll write it out just in case I goofed. I haven't touched Boolean algebra in over ten years and I haven't…
kayleeFrye_onDeck
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