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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Boolean algebra: why is $a\overline bc + ab = ac+ab$?

Why is $a\overline bc + ab = ab + ac$? I think it has something to do with the rule $a + \overline a = 1$, right?
SimonH
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Boolean algebra consensus theory

I want to simplify $wxy + x'z + y'z + wz = wxy + x'z + y'z$ but I can't seem to use the consensus theorem at the right place. I tried factoring cases for $x$ and $x'$ and $y$ and $y'$ but I don't know where to go. Can anyone give me just a hint…
maregor
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Finite boolean algebra can be embedded into $\mathcal P(n)$.

I am trying to show that every finite boolean algebra can be embedded into $\mathcal P(n)$ for some large $n$. Any hints?
user79594
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Reduce Boolean Expression

Note: A B = A and B A + B = A or B The expression: r = a̅ c̅ b + a̅ c b̅ + a c̅ b̅ + a c b Simplify?
A_for_ Abacus
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Simplification to DNF

To get right to the point. I have written a test which required me to Simplify to DNF. And the following equation gives me trouble. Here is the equation: ¬(¬x∨¬y∨¬z((x∨¬x)→0)→y So from there I went like this: => (x∨¬x)→0) => (¬x∨x)→0)…
Sipko
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Boolean Alegebra De morgans rule 2

hi i am told to perform a simplification using demorgans rule 2. Here is the question ' = Equals Not B . (C + B')' I got B' + (C' + B'') then B' + (C' + B) Now i dont know where to go from here. Could you guys please help. Thank You
Niel
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Precedence of nested NOTs in boolean algebra

I have the following equation: $y = \overline{\overline{\overline{x_{1} + \overline{x_{2}}} .x_{2}.x_{1}} + \overline{x_{3}.\overline{x_{1}+x_{2}} + x_{2}}}$ I'm trying to solve it in four ways: 1) From the outmost NOT to the innermost NOTs 2) From…
arnaudoff
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Single Complement Variable + 1

Is a complement + 1 = 1? For example A' + 1 = 0; I was thinking it was (I'm new to boolean algebra) since A' = 0, and 0 + 1 in boolean algebra is just 1. Of course, A can be anything, but assuming this is a single variable like B being represented…
ShrimpCrackers
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Simplify expression using boolean algebra laws

I can work out what the expression simplifies to and can show the equivalence with a truth table, but I don't know the law (or sequence of laws) that need to be applied to show this formally. This is the expression: ¬X OR (Y AND X) where ¬ is…
Matt
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how to simplify (x+y')X(x+z')?

Hi this is for a Discrete Math test I have today. I can barely understand the simplification of boolean expressions. Can anyone show me if the (x+y')X(x+z') can be simplified further, what are the steps? The original question is [x'(y+z)]'(x+y'). I…
Raphael Jones
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Prove that $x+(\overline{x}\cdot\overline{y})=x+\overline{y}$

Prove that $x+(\overline{x}\cdot\overline{y})=x+\overline{y}$ The values of both these boolean functions show that these 2 are equivalent. $x$ $\overline{x}$ $y$ $\overline{x}\cdot\overline{y}$ $x+(\overline{x}\cdot\overline{y})$ …
Sakthi
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expanding boolean expression as maxterm

$$ F = A + B'C $$ The expression has bothered. I've tried to expand the expression in maxterm, however, I'm stuck on the $B'C $ part. My approach is like this $$ = A + (B'B) + (C'C) + B'C $$ $$ = (A + B')(A +B) + (C'C) + B'C $$ then, $$ = (A + B' +…
AskQuestion
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3 input XOR gate

I have to implement a circuit following the boolean equation A XOR B XOR C, however the XOR gates I am using only have two inputs (I am using the 7486 XOR gate to be exact, in case that makes a difference)... is there a way around this?
Tap
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Basic Boolean Algebra Multiplication Question

I have the following term $$ t1: \overline {\overline{x1x2\Leftarrow\Rightarrow x1x3}\Leftarrow\Rightarrow x2x3} $$ which I already converted to this: $$ t2: ((x1x2\overline{x1x3} + \overline{x1x2}x1x3) \overline{x2x3}) + ((\overline{x1x2}x1x3 +…
MathiveProblem
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Simple Boolean Algebra Question

I have the following term in front of me: $$(AB+AC+\overline BC+B\overline C)*(A+\overline B+C+D)$$ and just need to multiply the whole thing which should result in this: $$(AB+ABC+ABD+AC+A\overline BC+ACD+\overline BC+\overline BCD+AB\overline…
MathiveProblem
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