Boolean algebras are structures which behave similar to a power set with complement, intersection and union. Questions regarding Boolean algebras as structures, or regarding functions defined from/to Boolean algebras fit into this tag very nicely. For Boolean logic use the tag propositional logic

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Simplifying this boolean function

How can I completely simplify this equation using algebraic simplification rules? $$x'y'z + x'yz + xyz$$
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196 views

Simplify Boolean Product of Sums Function

I've got a product of sums expression: F=(A'+B+C')&(A+D')(C+D') I need to show it as a sum of products and then simplify it. Right now I got: F=(A'&D')+(A&B&C)+(B&D')+(C&D') ...
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Boolean function on $\{0,1\}^n$ comprising just binary AND and OR gates

Let $f:\{0,1\}^n\to\{0,1\}$ be a boolean function computed by logical circuit comprising just binary AND and binary OR gates (assume that the circuit doesn't have any feedback). Let ...
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1answer
67 views

Truth table to prove statements

A, B and C. When questioned A says ''If B did not do it, then it was C." B says ''A and C did it together or C did it alone". C says ''We all did it together." How would i be able to put these into ...
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Every boolean algebra is the Lindenbaum algebra of a suitable theory

Can you suggest me a book/article/lecture notes where I can find informations about the topic: Lindenbaum Algebra and Boolean algebra? My purpose is to prove (or to sketch the proof of) the title ...
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34 views

Write $p \rightarrow \lnot q$ in CNF form with only and ,or and brackets

Write $p \rightarrow \lnot q$ in CNF form with only and, or, and/or brackets How on earth would I even do this? Completely lost! Any help appreciated.
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1answer
38 views

Boolean algebra (ISO)

Let $\mathfrak{A}$ be a Boolean algebra and $E$ be an element in $\mathfrak{A}$. The set of all subelements of $E$ forms a Boolean algebra, denoted by $\mathfrak{A}_E$. Suppose that $I$ be the ...
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57 views

Boolean formula vs boolean function.

Is there a technical difference between boolean formulas and boolean functions?
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41 views

How to simplify the boolean expression: $BCD+AC'D+A'BCD'+AB'D' +AB'C'D$

I have tried to simplify: $$BCD+AC'D+A'BCD'+AB'D' +AB'C'D $$ using logic rules, as well as multisim software, the last one says that the answer is $A'BC+AB'D'+AC'D+BCD$ Thanks.
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Translate Inequality to 2-SAT

How to translate Inequality, such as $A<B$ to $2-SAT$. I had an idea comparing the bits of the number but I failed implementing it.
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2answers
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How to simplify this using boolean algebra?

My paper is due tomorrow and there is only the last exercise left for me to do. However, I don't have any sufficient notes or examples on how to simplify it. Any help would be appreciated! A'B'C' + ...
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1answer
28 views

Explain one statement about Stone Space

In this page Stone Space This is no clear for me "The points in S(B) are the ultrafilters on B, or equivalently the homomorphisms from B to the two-element Boolean algebra" I think I means every ...
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1answer
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What is the underlying math in this relation?

Suppose we have the constraint $$.7x_1+.4x_2+.5x_3<1,$$ $$x_1,x_2,x_3\in\{0,1\}$$ Then we can convert it to a Boolean expression with binary variables of the form $$(\neg x_{1}\wedge\neg ...
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1answer
60 views

Can the obvious “product” of complete atomistic Boolean algebras be realized as a categorial product?

Let $X$ and $Y$ denote sets, and $\eta_X,\eta_Y : X,Y \rightarrow X+Y$ denote the natural injections to the disjoint union. Then intuitively, the "product" of the Boolean algebras $2^X$ and $2^Y$ ...
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1answer
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Boolean Algebra help [closed]

Establish the validity of the equivalence by using the Boolean properties attached. Only work on the left side. State the letter of the property you use at each step. $$(x\lor y)'\lor(x\land ...
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1answer
35 views

Convert a Boolean expression to a linear expression?

Suppose we have a Boolean expression $$(\neg x_{1}\wedge\neg x_{2})\vee\left(\neg x_{1}\wedge\neg x_{3}\right),$$ which we need to be true. Is there a method to convert this to a linear expression of ...
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1answer
98 views

How can I get a product-of-sums from this sum-of-products?

I have this function: $$f(A,B,C,D) = A'B' + CD' + ABC + A'B'CD' + ABCD'$$ I used a Karnaugh map to minimize the function to: $$Minimum SOP = A'B' + C D' + A B C$$ How can I turn this into a ...
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318 views

How to convert this Boolean expression to a NAND-only version using De Morgan's law?

I have a short Boolean expression which I have to convert to a NAND-only circuit, using De Morgan's theorem: a¬⊕(b∨c), i.e a XNOR (b OR c) I have started by applying the theorem to "(b∨c)", which ...
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1answer
24 views

Represent boolean OR opperator in non-boolean math notation

I'm trying to represent the boolean opperation OR in a regular formula, I am familiar with the boolean algebra notation, I came up with this (A+B)/(A+B) this works ...
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3answers
90 views

Can this Boolean expression be simplified any further?

I have simplified a Boolean expression to $$(\lnot a \land \lnot b \land \lnot c) \lor (a \land (b \lor c)).$$ Is there any way to simplify this further, e.g. using De Morgan's or anything?
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1answer
37 views

Proving that a given operator is universal.

I've got the next operator: $L(W,X,Y)=(W+Y)X'$ I need to prove whether the operator is universal, And if it isn't is: {$L,1$} or {$L,0$} are universal. I know that what i need to do is either ...
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3answers
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Where did I go wrong with this Boolean simplification?

I am completely new to Boolean algebra, and I've tried to simplify this expression. All I did is tried to follow my lecturers methods, but I don't think it's right, and I have no idea how to do it. ...
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0answers
66 views

How to write Propositional logic equation

Given $n-1$ teams and $m-1$ days, provide a propositional logic equation to illustrate the following: each team can only play 1 home game per day. All possible permutations must be played. I'm not ...
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37 views

Do these equivalence classes have any special property!

Suppose that $\lambda$ be a measure on the interval $I=[0,1]$, and Let $\mathcal{N}$ be the family of null sets. It is known that "measure algebra $\mathcal{B}$ " is the algebra of all measurable ...
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2answers
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My Boolean Expression Simplifications are correct or not?

1) I just want to know that my steps are correct or not? what are the missing steps. please help me. 2) Actually I can not simplify this is. So what are the missing steps at my trying path? please ...
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2answers
557 views

problem simplifying boolean algebra expression using consensus theorem

Please simplify this logic expression for me with helping boolean algebra : A'C'D + A'BD + BCD + ABC + ACD' I know that must use consensus theorem . my solve : STEP 1 : Terms 1 & 3 ...
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simplifying boolean algebra expression [duplicate]

A very urgent question : Please simplify this logic expression for me with helping boolean algebra : A'C'D + A'BD + BCD + ABC + ACD' I know that must use consensus theorem . my solve : STEP 1 : ...
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1answer
46 views

Boolean Expression Simplification

Dear all, I need help to simplify this Boolean algebra. Please give me a answer step by step. Thanks
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85 views

Find the disjunctive normal form of a function

so I am following in the textbook and have just been able to determine the disjunctive normal form of a function given a chart, but now these new questions say: ...
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0answers
29 views

What is the simplest form of the Boolean expression below? [duplicate]

I'm completely new to Boolean algebra, and I'm trying to simplify the expression below, using the distributive law, cancellation, negative absorption and De Morgan's theorem. I would start with the ...
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3answers
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Boolean endomorphisms vs endofunctions on finite sets

I stumbled upon a funny fact: Let $\mathbf{Bool} = \{0, 1 \}$. For all functions $f: \mathbf{Bool} \to \mathbf{Bool}$ it is the case that $f^3 = f$. This got me excited and I was wondering whether ...
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1answer
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How to give an assignment of boolean values such that this expression is evaluated to true?

Given the expression $E$, is there an assignment of boolean values ($true$ or $false$) that we can give to our variables such that this is evaluated to $true$? $E = (¬x + z + ¬v) · (¬v + w) ·(¬z + ...
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1answer
169 views

Convert expression to NAND only

Endless youtube videos and reading through notes later I am yet again stuck. I have to covert the following to NAND only $$\bar{A}\cdot\bar{B}\cdot\bar{C} + A\cdot\bar{B}\cdot C + A\cdot B\cdot ...
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Boolean Algebra simplify minterms

I have this equation $$\bar{A}\cdot\bar{B}\cdot\bar{C} + A\cdot\bar{B}\cdot C + A\cdot B\cdot \bar{C} + A \cdot B\cdot C$$ and need to simplify it. I have got as far as I can and spent a good 2 ...
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1answer
21 views

Demultiplexor Equation?

I am currently working on a project that requires a demultiplexor to be used. My problem is that I want to represent it in equation form, but no matter how much I try I cannot find the equation for a ...
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1answer
54 views

Inverse of a Boolean Function

Assume that I have a multi-output Boolean function $f(x_1,x_2,x_3,x_4) = (y_1,y_2,y_3,y_4)$. Is there a direct way of computing the inverse, that is, $g$ such that $g(y_1,y_2,y_3,y_4) = ...
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Simplify Sum of Products: $\;A'B'C' + A'B'C + ABC'$

How would you simplify the following sum of products expression using algebraic manipulations in boolean algebra? $$A'B'C' + A'B'C + ABC'$$
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simplify boolean algebra expressions

Use Boolean algebra to simplify the expression for F1, where, F1 = A’.B’.C’.D’ + A’.B’.C.D’ + A’.B’.C.D + A’.B.C’.D + A’.B.C.D’ + F2 and F2 = A’.B.C.D + A.B’.C’.D’ + ...
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Definition of a linear extension (total order?) of a poset

Hey I have a question about the definition of a linear extension of a poset. If I was given a hasse diagram of a poset with relation <= (S, <=), how can I get the compatible total order of this ...
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Hasse diagram vs digraph and bounds question

I have attached a link to my hasse diagram I drew... Sorry about image size and rotation. So is it correct to say a hasse diagram is just a digraph with each internal vertice removed? So would my ...
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1answer
40 views

Convert 4-sat to 3-sat

I want to know in general how can I convert $4-SAT$ to 3-SAT. And I have a specific case that if you can help me optimize it to 3-SAT it will be greate. I want to do this so I be able to use sat ...
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1answer
91 views

How to prove this equality using boolean algebra?

I have approximately no idea on how to solve the following problem, so any help would very much be appreciated: $$x' y'+ x y = (x y' + x' y)'$$ I can't figure out how to prove the equalities ...
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2answers
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Boolean Algebra - Why is the result 1?

Given: = !(A * (!B + C)) + !(!B * !C) = !A + (B * !C) + !B + C Where: ! = NOT + = OR * = AND I'm having some trouble to why !A + (B * !C) + !B + C simplifies to 1? Can someone shed some light on ...
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Doubt in K-map rule (loops)

Is it possible to mark a loop in k-map as in second figure in above diagram (indicated in blue). According to my knowledge the first figure is correct. Is figure 3 or 4 correct? Note: Consider ...
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Cantor-Bernstein theorem for $\sigma$-complete Boolean algebras.

I am working on problem 7.28 from Jech's Set Theory: Let A and B be σ-complete Boolean algebras. Let a and b be elements of A and B respectively. If A is isomorphic to B$\upharpoonright$b and B is ...
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2answers
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How to write this as a boolean expression?

How can I write the following sentence as boolean expression: $$ \text{If two sides of triangle are the same, then two opposite angles are the same} $$ I konw it should be something like this: $$ a = ...
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Convert Circuit SAT to 3-SAT

I am trying to convert Integer Factorization to $3-SAT$. So far I managed to convert it to Circuit SAT, but I don't know how to make the final step. This is how it look for 3*3 multiplication: ...
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1answer
31 views

Homework: Conjunctive Normal Form

The way I understand CNF is as an expression containing AND's of OR's. So an AND-GATE with 3 inputs (A, B and C) should just be A AND B AND C. But apparently this is incorrect. Any guidance would be ...
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Fields of sets in which, if the l.u.b. of a subset exists at all, it is the union of the subset

I am learning about boolean algebras and how they can be represented as fields of sets. Stone's representation theorem tells us that every boolean algebra is isomorphic to a field of sets. Consider an ...
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Prove This Bool Expression

Prove $x'z+xyz+xy'z=z$ can you show how you solve this using Boolean Algebra. My main problem is when I do this $xz (y + y') = 1 $ So $1$ times $x =$ ?