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 .

3083 questions
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How to simplify $A(\overline BC+B)$

How do I go from $A(\overline BC+B)$ to $A(B+C)$? What definition should I use to get the final answer? Would like an explanation and proof so I can learn rather than just memorise.
NLed
  • 301
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Boolean Simplification Problem

I have to simplify the figure I came up with the equation $$(ac+\bar b)\cdot (a+b+\bar c) \cdot (b+ac).$$ Help me out Attempted Answer: \begin{align*} (ac+\bar b)\cdot (a+b+c)\cdot (b+ac) &=(ac+abc+ac+a\bar b+\bar b…
k31453
  • 21
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Trying to simplify $A'B'C'D + A'B'CD + A'BC'D + AB'CD + ABCD$

My solution so far: $A'(B'C'D + B'CD + BC'D) + A(B'CD + BCD)$ $= A'(C'D(B' + B) + B'CD) + A(CD(B'+B))$ $= A'(C'D(1) + B'CD) + A(CD(1))$ $= A'C'D + A'B'CD + ACD$ $= D(A'C' + AC) + A'B'CD$ $= D(A\text{ xnor }C) + A'B'CD$ $= D[(A\text{ xnor }C) +…
KrispyK
  • 71
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Simplify Boolean Expression ABC' + A'BC + A'B'C'

Can anyone help me simplify this boolean expression? ABC' + A'BC + A'B'C' EDIT: (only using AND gates (multiply [(x)(x)]) and OR gates (addition [+]))
Jiyugata
  • 21
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Solving Boolean Expressions with Theorems

I'm having the hardest time wrapping my head around this stuff. This is a homework problem, one of many. I just need some help on what to do. BC + A'B' + A'C' = ABC + A' I've tried this: BC + A'(B' + C') = BC + A After this my erase marks get more…
Jerrod
  • 155
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Can a minimal representation of a Boolean Function be 1 or 0

After using the Karnaugh map to find the minimal representation of a Boolean function, my answer is 1. Is 1 a valid answer for minimal representation? If yes, what is the implication of a Boolean function has 1 as its minimal representation?
WingLeo
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Need help for right direction simplifying boolean algebra formula

I have the following boolean algebra, where union is $+$ and intersection is $\cdot$ : $(x\cdot y)+((z+y)\cdot \bar{z})+y=y$ Is there a systematic way of doing this, or do you need to puzzle? My train of thought would be to see if I could get rid of…
user94450
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Simplify Boolean Expression A'B'C + A'BC + AB'C

The K-map method of simplifying the Boolean Expression A'B'C + A'BC + AB'C gives the answer to be A'C+B'C. But I am not able to solve this algebraically. Please help me out. What I have tried is A'B'C + A'BC + AB'C = A'C (B'+B) + AB'C = A'C(1) +…
mohd shoaib
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Does Huntington's axiomatization of boolean algebras include idempotence?

In different places Huntington's axiomatization of boolean algebras is $x\vee y=y\vee x$ for all $x$ and $y$, $(x\vee y)\vee z=x\vee(y\vee z)$ for all $x$, $y$ and $z$, $(x'\vee y)'\vee(x'\vee y')'=x$ for all $x$ and $y$. I am not able to show…
Joel Adler
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Convert a boolean expression to just NOR operatons

How do we convert this expression to just $\text{NOR}$ operation? $$A \cdot B + B \cdot C + C \cdot D$$ My attempt: $A \cdot B + B \cdot C + C \cdot D = \overline{\overline{A \cdot B + B \cdot C + C \cdot D}} $ Using De Morgan's law $ \to…
Node.JS
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Simplification of expression $\bar{x}\bar{y}\bar{z} + \bar{x}\bar{y}z+x\bar{y}\bar{z}+x\bar{y}z$

Here are my steps: $\bar{x}\bar{y}\bar{z} + \bar{x}\bar{y}z+x\bar{y}\bar{z}+x\bar{y}z$ $$\bar{x}\bar{y}\bar{z} + \bar{x}\bar{y}z+x\bar{y}\bar{z}+(x\bar{y}z+x\bar{y}z)$$ Used Idempotent law and rearranged the equation $$\bar{x}\bar{y}\bar{z} +…
Dravid
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Boolean Algebra - is this statement correct?

So I have a statement that goes like this: $$ ( \lnot A \lor B) \land(\lnot A \lor \lnot B) $$ I think it is equivalent to $$ \lnot A $$ Am I right or not?
GawronDev
  • 23
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Boolean Algebra: How to simplify $ab + ac + \bar a \bar b c$ algebraically?

In the boolean logic $ab + ac + \bar a \bar b c$ is equivalent to the simpler $ab + \bar b c$ This can be confirmed by looking at the truth table (below). The $ab$ and $\bar b c$ minterms cover the $ac$ minterm. My question is, in general/practice,…
joseville
  • 1,477
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Existence of $\sigma$-ultrafilters on free $\sigma$-algebra

Suppose that $A$ is a free $\sigma$-algebra on a countable set of generators. Does $A$ have a $\sigma$-ultrafilter? I have no difficulty in proving that $A$ contains at least an ultrafilter. For example, consider the set $F$ of all non-zero elements…
Beginner
  • 574
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I cant smplify the five variable boolean algebra.

I've tried for many times to simplify the five variable boolean algebra but can't get it done. Question $$F = \bar{A}\bar{B}\bar{C}\bar{D}E + \bar{A}\bar{B}C\bar{D}E + \bar{A}B\bar{C}\bar{D}E + \bar{A}BC\bar{D}\bar{E} + \bar{A}BC\bar{D}E +…
Asir Shahriar Roudra
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