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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 .

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How to Solve The Redundant Literal Rule (AND)?

(A . B = A . (A̅ +B)) How to prove them? (Tried so many times)
Bachi Nirosh
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How to prove distributivity in Boolean Rings

A Boolean ring is a ring which all of its elements are idempotent, i.e. $a ^{2}=a$. I know that If we interpret multiplication and addition in such a ring, as meet and joint respectively, then Boolean Ring is essentially the same as Boolean Algebra.…
user34942
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Boolean Simplification

I'm having some trouble getting a handle with this course. We are starting Boolean algebra and my professor wants us simplify the following: (AB)'+(A'+B')'= (AB)'+BC+A'B'C'= I am assuming the "()" with "'" means the over-score above the…
Leo
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Is this simplification correct, and if so, what law does it illustrate?

Can I simplify $(F \land \neg M ) \lor (F \land A) \lor (F \land M \land G)$ to $F \land (\neg M \lor A \lor (M \land G) )$ ? And if so, what law does this illustrate?
Baodad
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Boolean Algebra Distribution

I have some boolean algebra I preformed, but it does not appear to be right, and I am unable to justify to myself why. $$F=(a+b+c)(a+b+d)$$ $$F'=(a'b'c')+(a'b'd')$$ $$F'=(a'b')(c'+d')$$ $$F=(a+b)(cd)$$ Yet if I let $a=c=d=0$ and $b=1$,…
Christopher Crutchfield
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Prove equivalence of 2 boolean functions

I'm struggling with proving that theese 2 boolean functions are equivalent. $$(a \vee b) \equiv c$$ $$(a \equiv c) \equiv (b \Rightarrow a)$$ I'm not allowed to use truth tables or Vienn diagrams. My teacher told me that I need to get one of the…
Сергей Позняк
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Proving $A+A'B=A+B$ without truth tables

How can I prove the Boolean algebraic rule $$A+A'B=A+B$$ without using a truth table? With the truth table, it is easy to see that the two are equal, but how can I prove it using lesser Boolean identities?
Zak Bagwell
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Boolean algebra with the definition of Huntington - prove de morgan's law without the use of associativity

I started with the definition of boolean algebras by Huntington, which is: A boolean algebra is a set $B$ with two operations on $B$, so that for all $a \in B$, $b \in B$ and $c \in B$ holds: Commutativity:…
Jonny
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How can this expression be simplified using boolean algebra?

So I have this expression: $$ A'BD + B'C' + AC' + C'D $$ How can I simplify it using boole's algebra? I figure out the $C'D$ is included in the other terms through Karnaugh maps but I can't figure out the simplification.
Carlos Sá
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Get Peanos definition of a boolean algebra from the definition of Huntington.

I have the following definition: A boolean algebra is a set $B$ with two operations on $B$, so that for all elements $a \in B$, $b \in B$ and $c \in B$ holds: Commutativity: \begin{equation}\label{1.1.1} a \land b = b \land…
Harald Meisner
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Let A and B be any propositional formula

How can I prove the following? If $A$ is a tautology and $A\implies B$ is a tautology, then $B$ is a tautology.
jjAbrahams1
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Prove Equivalence of A’D+BCD’=(D+B)(C+D)(A’+D’)

I need to prove that two expressions, obtained from Karnaugh maps, are equivalent. So far I have A’D+BCD’=(D+B)(C+D)(A’+D’) A’D+BCD’=(DC+BC+DD+BD)(A’+D’) A’D+BCD’=A’DC +A’BC+A’DD+A’BD+D’DC+D’BC+D’DD+D’BD A’D+BCD’=A’DC…
Emilio Garcia
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Simplify Boolean Expression Help

I have a question: is this true the way I solve it? $$\begin{align*} xyz&+xyz'+xy'z+xy'z'+x'y'z+x'yz'\\ &= xy+xy'+x'y'z+x'yz'\\ &= x(y+y')+x'y'z+x'yz'\\ &= x+x'y'z+x'yz'\\ &= x+x'z'z\\ &=x \end{align*}$$ Am I doing something wrong here?
Donny Avaris
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Boolean functions question

I am trying to solve exercise 1.29(a) from Ryan ODonell's Analysis of Boolean Functions which says that given $ f:\mathbb{F}_{2}^{n} \rightarrow\{-1,1\} $ such that $ dist(f,\chi_{S^{*}})=\delta $ for some $ S^{*} \subseteq \{1,2,...,n\}$where $…
Andrei
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Do I have to convert from product of sums to sums of products, and how to find minimal sum of products from truth table?

I have been trying to solve this problem but I am unsure whether or not this is the right procedure. I have the following truth table. Truth Table I need to find the expression for F as a product of sums and as a sum of products. I also need to find…
Brandon Chung
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