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

learn more… | top users | synonyms

0
votes
1answer
22 views

Boolean expression explanation

Could someone explain how to get the following Boolean expression in its simplest form, I am having difficulties working it out step by step $$A+B+A*B$$
1
vote
1answer
27 views

Boolean functions- depth of generated function and info

I'm looking for a general book/link to information about boolean function (Function from to {0,1}), we've introduced them in a logic course but it seems we won't focus on them.
1
vote
2answers
56 views

Boolean Algebra - Prove XYZ + XYZ' + XY'Z + X'YZ = XY + XZ + YZ

Trying to prove $((X\land Y\land Z)\lor (X\land Y\land \lnot Z)\lor (X\land \lnot Y\land Z ) \lor (\lnot X\land Y\land Z)) \equiv ((X\land Y)\lor (X\land Z)\lor (Y\land Z))$ and I am a bit stuck. I ...
1
vote
4answers
38 views

Boolean Algebra - Xor simplification

I have a boolean equation: $e(g \oplus (g + b))$ and it is simplified to $e(\lnot g)b$. I do not see how this simplification is done. What i did was the following: $e(g \oplus (g + b)) --> e(g(\...
0
votes
1answer
38 views

Do we complement Boolean variables in the Dual?

The Principle of Duality states that starting with a Boolean expression, another Boolean expression can be obtained by : 1. Changing OR to AND 2. Changing AND to OR 3. Changing 0 to 1 4. Changing 1 ...
1
vote
2answers
31 views

Simplifying a Boolean algebra equation

I have a boolean algebra equation that i'm not able to simplify fully. \begin{align} &(c+ab)(d+b(a+c))\\ &(c+ab)(d+ba+bc)\\ &cd+ abc + bc^2+abd+a^2 b^2 + ab^2 c\\ &\text{using boolean ...
0
votes
1answer
20 views

Delove the truth for the three function same table

Given Boolean functions: $F(x,y,z)=x'.(y'+z')(x+y'), G(x,y,z)=x'.(z+yz')(x\oplus zy')$ Develop the truth table for the three function in the same table
3
votes
2answers
66 views

Who is Petrick from Petrick's method?

I would like to ask your help. I think this is the best place for this. In my language -as well as English- I haven't found anything about Petrick yet. His method okay, but I would like to know about ...
-1
votes
1answer
30 views

Boolean Algebra Problem [closed]

$ab+(ac)'+ab'c(ab+c) = 1$? how ?
7
votes
1answer
117 views

Existence of surjective homomorphism between Boolean algebras $\Lambda\subset\mathscr P(\mathscr B)\to\mathscr B$ (in ZF)

I am trying to prove the following theorem, due to Tarski according to W. A. J. Luxemburg on Reduced powers of the real number system and equivalents of the Hahn-Banach extension theorem: Given a ...
0
votes
0answers
36 views

Does this always evaluate to true?

This expression: $1 \lor (0 \land 1 \land 1 \land 1 \land 1 \lor 0)$ Regardless of how order of operations inside the parentheses are taken, which are ambiguous, the fact that it is and Or operation ...
0
votes
0answers
11 views

Order of Galois connections between two boolean lattices

Is the poset of Galois connections between two boolean lattices itself a boolean lattice? If not, does it hold for: complete boolean lattices? atomic boolean lattices? atomistic boolean lattices?
0
votes
0answers
99 views

Galois connections between boolean lattices - an alternative representation

Let $\mathfrak{A}$ and $\mathfrak{B}$ be (fixed) boolean lattices (with lattice operations denoted $\sqcup$ and $\sqcap$, bottom element $\bot$ and top element $\top$). I call a boolean funcoid a ...
1
vote
0answers
33 views

Two alleged counterexamples (about boolean algebras)

Trying to solve this question, I propose two possible counter-examples. Please help me to understand whether these cases are really counter-examples. Let $\mathfrak{A}$ and $\mathfrak{B}$ be (fixed) ...
0
votes
1answer
17 views

More on a construction on two boolean lattices

Let $\mathfrak{A}$ and $\mathfrak{B}$ be (fixed) boolean lattices (with lattice operations denoted $\sqcup$ and $\sqcap$, bottom element $\bot$ and top element $\top$). I call a boolean funcoid a ...
1
vote
1answer
26 views

Boolean lattices vs boolean rings

Which kinds of theorems about boolean algebras are easier to prove with boolean rings (than with actual boolean lattices)? Give me at least one example, as an answer.
0
votes
0answers
16 views

Counting self dual functions

The dual of a function is defined as the same function with and/or operators exchanged .A function is self dual if dual of function and function itself are same.How many maximum self dual functions ...
0
votes
1answer
27 views

Simplifying a boolean expression without using sum-of-products

Yes this is for a school class, and no I'm not asking anyone to do my homework. This is from an example. I have a boolean algebra expression that I have to simplify. I also have the answer simplified ...
1
vote
1answer
38 views

Implement boolean function with OR-NAND and NOR-OR gates

This is the boolean function: F(A,B,C,D) = Σ (0,4,8,9,10,11,12,14) and so after using a K-map to minimize it, I came out with F(A,B,C,D) = C'D' + AB' + AD'. Now the other two parts of the problem were ...
0
votes
0answers
26 views

Boolean Algebra, simplify expression

I've been trying to simply this expression but all I have managed to do is get rid of a D'. I assume there must be more I can do but I can't find out what I'm supposed to do to it. If you can help me ...
0
votes
1answer
22 views

Boolean Algebra, Proving expression

I've been struggling to prove this expression literally all day please help. A'B + A'C + B'C = A'B + B'C
0
votes
2answers
23 views

Simplify expression in Boolean algebra

In Boolean algebra, I need to prove that $AB+AB'C+BC'=AC+BC'$ and $(ABC)'(A+B+C)=A'B'C'$ Are both the questions correct?
1
vote
1answer
40 views

Boolean Algebra- Simplification

I'm attempting to simplify this and don't know if I'm doing it right. This is the problem: (a+b+c')(a'b'+c) Attempted solution: ...
3
votes
1answer
67 views

Negation of XOR

I feel pretty confident with expanding an XOR, but when it is negated, it throws me for a loop a bit. The problem I am trying to prove: $$\overline{x_1 \bigoplus x_2} \bigoplus x_3 = \bar{x_1}\bar{...
0
votes
1answer
22 views

Write PQ' in the form A'+B

I'm trying to find the negation of the sentence "All domestic cars are good". The sentence can be rewritten as "If a car is domestic, it is good". if P then Q is the boolean expression - P'+Q. The ...
1
vote
0answers
65 views

Simplifying bitwise expressions

Using various methods it is possible to simply boolean expressions consisting of boolean operators and binary variables. In programming languages another closely related set of operators exists: ...
1
vote
1answer
76 views

Prove the following boolean identity using Consensus theorem.

I have been trying to prove it for last 4 hours but couldn't find a solution. Please help me. $$(A+B')(B+C')(C+D')(D+A')=(A'+B)(B'+C)(C'+D)(D'+A)$$ I solved and got the following answer. $$(A'+B)(B'...
1
vote
1answer
50 views

If $*$ a functionally complete logical operator then $tautology *tautology $ is contradiction.

Would anyone please give me a hint to prove that if $*$ is a functionally complete binary connective and $@$ is a symbol for tautology, we must always have $ @*@$ is equivalent to contradiction (I ...
1
vote
1answer
63 views

Free product of the powerset algebras of group orbits. Interpretation

I am trying to interpretate the following sentence in the context of measures on groups and algebras, from J. Pawlikowski on "The Hahn-Banach theorem implies the Banach-Tarski paradox" Let $F$ be ...
0
votes
2answers
23 views

Resolution of a Boolean Function

I have to solve this simple boolean function : $$f_1 * f_2 = (x_1 + x_2) * (!x_1 + x_3)$$ The solution is : $x_1*x_3 + !x_1*x_2$ Can anyone make a step by step solution because after getting : $$...
1
vote
1answer
40 views

All possible set operations between sets

I was looking for some sort of generalization on set operations between different sets, and how that number of operations increases as the number of set increase as well. It can also be thought as the ...
1
vote
4answers
36 views

Simplify the boolean function below by using algebra laws.

I've been stuck on this question for some time, if anyone happens to solve it please explain step by step. $$(A +B ) \times ( A' + C ) \times ( B + C )$$
3
votes
1answer
73 views

Intuition for power-set structure of finite Boolean rings

A course I am taking has started to introduce Boolean rings: rings where every element is idempotent. It was proved that every finite Boolean ring $R$ is isomorphic to a power set ring $\wp (S)$ for ...
-3
votes
1answer
66 views

Why are there two different notations for negation in boolean logic?

For the boolean variable $x$, there are two notations for its negation: $\neg x$ and $\bar x$. So why are there two different notations?
0
votes
2answers
113 views

Karnaugh map and Circuit of a full adder

I have the following task: The addition can be implemented by the rules 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 10. Full addition requires carry-in and ...
1
vote
2answers
55 views

Boolean equation

$$\text{Solve for}\space{x, y}$$ $${a_1, a_2, a_3, a_4, b_1, b_2} \; \text{ - variables}$$ $$\left\{ \begin{aligned} {a_1}\&x \oplus {a_2}\&y &= {b_1} \\ {a_3}\&x \oplus {a_4}\&y ...
0
votes
1answer
39 views

Is there a proof for the FOIL method in Boolean algebra?

The FOIL method is the special case of multiplying algebraic expressions using the distributive law and is shown here: What does the proof for this look like using Boolean algebra?
0
votes
0answers
23 views

m-bit parallel adder needed using full adder

How many full adder is needed to construct a m-bit parallel adder? I have construct a 4-bitparallel adder with 4 full adders. but can the number be reduced?
0
votes
0answers
30 views

Need help on clarification on a boolean algebra/logic gate question.

The question asked on my homework. I have a question on my home work that is confusing me. I went through and made a truth table and found the all of the values corresponding to the minterms that ...
1
vote
1answer
19 views

Can you simplify this Boolean expression any farther?

I was working through a problem for a Computer Engineering course and i was given this logic function F(A,B,C,D) = ~A~BC~D + ~AB~C~D + ~ABC~D + ABC~D After ...
0
votes
0answers
31 views

An intuition connected with Heyting implication

Suppose $L$ is a bounded lattice and let $\Rightarrow$ be its Heyting implication, i.e. the operation defined in the standard way: $x\Rightarrow y$ is the largest object of the set $\{u\in L\mid u\...
0
votes
3answers
38 views

Boolean Algebra - $ABC+B'=AC+B'$?

I'm doing a bit of homework, and it says to prove or disprove the statement $XZ+X'Y'+Y'Z'=XZ+Y'$ If you do a truth table and take the sum-of-products, you can eventually simplify the equation down ...
1
vote
1answer
13 views

Help with Boolean expression simplification with $4$ variables.

I've simplified this expression and am unsure if it's completely simplified. If it can be simplified, can you provide me with the answer and the steps/laws taken to do so? Thank you. $y’(z+x)+z’(xw+x’...
2
votes
2answers
24 views

Simplifying 4-term Boolean Expression

I am given a pretty lengthy Boolean expression: $$(¬A ∧ ¬B ∧ ¬C ∧ ¬D) ∨ (¬A ∧ B ∧ ¬C ∧ D) ∨ (A ∧ ¬B ∧ C ∧ ¬D) ∨ (A ∧ B ∧ C ∧ D)$$ which I am asked to simplify. The solution should be: $$((¬D ∨ B) ∧ ...
0
votes
1answer
71 views

Binary to Gray code using XOR boolean expressions

I have a question which asks to design a circuit to convert from binary to gray code, using a boolean expression. Now I understand you have to use XOR to achieve this. And I understand that XOR ...
1
vote
1answer
24 views

I need prove a boolean function

In need to prove with boolean algebra that XOR complement (negado) is equal to XNOR but i cant do it, can you help me? !(!xy+x!y)=xy+!x!y how to prove it?
0
votes
1answer
43 views

How to solve binary equation which has mod?

Three messages in binary format are sent $$ a_0 a_1 a_2 a_3 $$ and coded in binary format $$b_0 b_1 b_2 b_3 b_4 b_5 b_6$$ Symbols $$b_0,b_1,b_2,b_3,b_4,b_5,b_6$$ are the coefficients of the Boolean ...
0
votes
1answer
31 views

How to prove that any Boolean function can be simulated only using AND gate and NOT gate?

I want to see how to prove the functional completeness of NAND gate, but all the materials in the web I have reached just relies on the fact that the set $\{AND,NOT\}$ is complete and shows how to ...
0
votes
1answer
21 views

Representing Boolean expressions in a truth table.

Right so I'm trying to understand truth tables in the context of digital logic. And paticularly with lettered boolean expresssions. Now I do understand truth tables, you have either true or false as ...
0
votes
2answers
45 views

How does one simplify this boolean expression?

(a + b)(b' + c')(a + b' + c) where b' = b not and c' = c not. I tried distributive because I'm not very good at applying the properties when multiplication is applied but I can with addition. (a + ...