Mathematics Stack Exchange
Mathematics Stack Exchange

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 .

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How is $F = xy + x'z = (xy + x')(xy + z)$ deduced in Boolean Algebra?

I am given a function $F$ such that: $$F = xy + x'z$$ In a solution of an example, the following is done. I am trying to understand how the author deduced this result. Only thing explained is that distribution law was used. $$F = xy + x'z = (xy +…
Haggra
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Boolean Algebra Manipulation/Simplification

I have come across a couple questions while doing my digital logic work. 1) Is it possible to simplify these, while keeping each a product of sums? (I'm leaning towards no--the only way I could see to simplify them would be to distribute.) They're…
RyanB
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How a Boolean Algebra is a $\bf F_2-$ Vector Space?

In a answer of this question it's said that "A ($\sigma$-)algebra is a boolean algebra. In particular, it is an $\Bbb F_2$ vector space." Unfortunately i have never seen this term Boolean Algebra.Could someone please explain me what is a Boolean…
Dontknowanything
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Disjunction as sum operation in Boolean Ring

Boolean ring is defined with operations of ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). I understand that algebraic structure involving…
Tegiri Nenashi
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Boolean Algebra Karnaugh Maps

I'm having trouble solving this: Simplify the expression F = W'X'Y'Z' + W'X'YZ' + WX'Y'Z' + WX'YZ' + WXYZ + W'XYZ using a Karnaugh Map. The book I have very poorly describes how to do Karnaugh Maps. I'd appreciate any help.
Wouter
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Boolean expressions from multiplication to addition and vice-versa

I am trying to change these Boolean expressions into expressions that do not use multiplication. Bolds indicate complements. a) abc b) (ab +c)d And these to ones that do not use addition. c) a + b + c d) (ab + c)d + e How should I approach these…
kvax12v
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How would one solve this boolean algebraic equation?

During software testing I needed to find at least one solution for this: (a or (b and c)) != ((a or b) and c) Where all variables are boolean. I can (and did) solve it with brute-force (if you can call so few combinations brute-force): for a in…
Elliot Chance
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Each Element of an Algebra can be Partitioned into "Atoms"

Let $\Omega$ be any set and let $\mathcal A$ be an algebra of sets in $\Omega$. An element $E\in \mathcal A$ is said to be an atom if there is no non-empty element $A\in \mathcal A$ such that $A\subsetneq E$. (By convention we allow $\emptyset$…
caffeinemachine
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simplifying boolean expression in minterm

i am trying to simply the equation and stuck. Sum symbol(2,4,6,7). It means $$ F = A'BC' + AB'C' + ABC' + ABC $$ $$ = A'BC' + AB'C' + AB(C' + C) $$ $$ = A'BC' + AB'C' + AB $$ After the last equation part, I haven't gone on. Did I choose wrong way…
AskQuestion
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How to simplify the Boolean function $A'B'C + A'BC' + ABC + AB'C'$?

So the question I have asks to implement the circuit with $XOR$ gates. So I am 3/4 through the problem when I am having problems simplifying the Boolean expressions below: $$A'B'C + A'BC' + ABC + AB'C'$$ According to the professor this can be…
George Nehme
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What is the most simplified form of $y(x′z + xz′) + x(yz + yz′)$

I am stuck on a problem that I know the logical answer to, yet I cannot seem to simplify properly to get there. I want to simplify $$F(x,y,z)=y(x′z + xz′) + x(yz + yz′)$$ I know the simplest form (using a truth table) is $$xy + yz$$ Yet my…
Elliott
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Boolean and equivalent to summation

Is there a mathematic symbol to express the application of AND operator to a set of booleans, that returns true only of all booleans in the set are true. Something like the summation operator on a set of integers.
Daniel Cerecedo
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How should I think when implementing Patrick's method?

I have implemented Quine-McCluskey method of boolean function simplification. I ended up with the table of prime implicants: As you can see my results are the same as these on wikipedia. However now I need to create the simplest formula using the…
Tomáš Zato
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Boolean Algebra Minimization

Prove that $\bar{A}B + AC + BC = \bar{A}B + AC$ with the help of boolean algebraic manipulations. I have no clue from where to start, how should I tackle these type of questions? Or $$ \left(\neg A \wedge B\right)\vee \left(A \wedge…
Soham
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Intuition behind duality principle?

I'm looking for an intuitive explanation of the duality principle. I found this proof but it was way above my head, considering I just started Boolean Algebra a couple of days ago. I suspect most proofs will be above my head, so can someone help me…
John Cranson
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