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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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Boolean algebra simplification

I have the equation (CD)+(BC'D'+A'B'C'D)+(C'D') and I can't seem to simplify it enough for my homework. I've tried multiple ways of simplifying the equation and I keep ending with an extra variable D.
Lo0GiC
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sum-of-products expansions of these Boolean functions

Find the sum-of-products expansions of these Boolean functions. $a)$ $F(x, y) = \text{~}x + y$ $b)$ $F(x, y) = x \text{~}y$ $c)$ $F(x, y) = 1$ $d)$ $F(x, y) = \text{~}y$
Reem
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Boolean-expression simplification F = [ AB ( C + (BC)' ) + AB' ] CD'

Basing on that problem. All I have in my solution is this: mystep1:[AB(C +(B' + C')) + AB']CD' mystep2:[AB(CB'+ CC') + AB']CD' mystep3: [AB(CB') + AB']CD' mystep4:[B(A+C+B') + AB']CD' mystep5:[AB + AC + AB'] CD' mystep6:[AC]CD' mystep7: ACD' F =…
Sha Lala
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Correctness of answers and question about sup en inf

In $A=\{2, 3, 6, 12, 36, 72, 108\}$ we define the relation $R$ by $aRb$ if $b=a$, or $b=2a$ or $b=3a$. Q1: Draw the graph of $R$ and list which properties $R$ has. A1: The properties are: reflexive, anti-symmetric, and non-transitive. Q2: Determine…
Garth Marenghi
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How to prove boolean ordering question

Let $\sqsubseteq$ be the boolean ordering of $X$, so for every $x$ and $y$ applies $x \sqsubseteq y$ if $x \sqcap y = x$. Let $v, w, a, b \in X$ with $v \sqsubseteq a$ and $w \sqsubseteq b$. Show that $v \sqcup w \sqsubseteq a\sqcup b$ and $v \sqcap…
Garth Marenghi
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How do I solve this Boolean Algebra Problem?

Let A be an arbitrary but fixed Boolean algebra with operator $@$ and $*$ and $'$ and the zero and unit element be denoted by $0$ and $1$ respectively. let $x,y,z \in A$ if $a,y \in A$ such that $x*y=0$ and $x@y=1$ Then prove that $y=x'$
Aman Mittal
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Boolean Algebra Syntax

Six alphabets, A,B,C,D,E, and F have to be arranged in six numbered positions(1-6). How many ways can you arrange them so that A is not in position numbered 1 , B a is not in position numbered 2 and C is a is not in position numbered 4. I am trying…
jessica
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Help with getting the right direction on a boolean algebra question

Need some help getting in the right direction for answering the following question: Prove the following property and interpret this in $\mathcal P \left ({V} \right)$: if $x+ \bar y=$ 1, then $x+y=x$. How can I best approach this?
Garth Marenghi
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Boole Algebra, ab+bc+ca=(a+b)(b+c)(c+a), how to solve starting from left?

I was able to find a demonstration, starting from the right part, I wanted to start from the left part, in order to check if I understood well my knowdlege, Starting from left or right does make any difference in how it's complex the resolution?…
Delayer
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Variable elimination by clause distribution in Conjunctive normal form (CNF)

I am refering to this document. The relevant part is: My question: I understand that (a or b) and (not(a) or c) implies b or c but what really confuses me is the statement "The produced resolvents $S{'} = S_x \circ S_{\overline{x}}$ replace the…
mangolassi
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A questions on complete endomorphisms of $2^{\mathbb{N}}$

Let $A$ and $B$ be complete Boolean algebras and $f:A\to B$ a homomorphism. Recall that $f$ is complete if $f$ it preserves arbitrary (including possibly infinite) joins. Does there exist a non-complete endomorphism of $2^{\mathbb{N}}$ that…
Jordi
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Simplifying Boolean Algebra - factorising

How is: $P \lor ¬Q \lor P \land ¬Q$​ Factorise​d to get: $P \lor ¬Q \land (1 \lor P)$ I've been staring at it all weekend. I understand what factorisation is and can do it in math. I tried expanding it to get: P v ¬Q ^ v P v ¬Q ^ P It makes no…
user252704
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Why does A'B'C' + ABC not equal 1 due to the boolean algebra law X' + X = 1?

I am learning boolean algebra, but this is confusing me. How does A'B'C' + ABC not equal 1? If you do the truth table for ABC then the output will not always be 1, for example 101 gives an output of 0. Why is this? Why can't we use the law X' + X =…
Trev347
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Boolean algebra: Why is $(x'\lor y')(x' \lor y)\equiv x' \lor y'y$?

Perhaps they've skipped some steps?
Jason Xu
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How to prove below two logic formulas?

Below 2 formulas are used for SM3 algorithm, first one is FF2 & second one is GG2. FF2(X,Y,Z) = $(X \land Y) \lor (X \land Z) \lor (Y \land Z)$ GG2(X,Y,Z) = $(X \land Y) \lor (\lnot X \land Z)$ And I also found some implementations used below…
Emman Sun
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