# Tagged Questions

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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### Is the tensor product of BAOs a kind of extended BAO?

I've been reading "Boolean algebras with operators. Part I." (Jonsson, Tarski) where, given a subalgebra of a Boolean Algebra, they define its perfect extension. As far as I understand it can be ...
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### Karnaugh map grouping of element

In Karnaugh map ($4\times 4$) can we group an element that is shared two three different groups. I think answer should be no but I do not know why it is?Can anybody provide a reason in support of this ...
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### Memory and bits. Need some help

Could someone check over my answers to verify I am correct. Say we have a memory consisting of 2048 locations, and each location contains 16 bits. ◦ A) How many bits are required for the address? ...
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### Is there a way to reduce a set of linear inequalities representing a set of vectors in $\{0,1\}^n$?

Given a fixed number $r$, such that a vector $v_i \in \{1,0\}^n$ has exactly $r$ ones and $n-r$ zeroes, and a number of inequalities, (say $I$ is this set of inequalities) representing a set $J$ of ...
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### Fourier Analysis for Derandomization of Functions

I was wondering if there was an extension to Fourier Analysis on Boolean Functions. Specifically, it's well known that for any boolean function $$f: \{-1,1\}^{n} \rightarrow [-1,1]$$ we can decompose ...
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### How can I find a DNF and Minimal Form for this boolean expression?

$Q(x,y,z)=(y′\vee z′ \vee 0\vee x′)\wedge1\wedge(z\vee x′\vee 0\vee y\vee z)′\wedge(z′\vee x\vee y\vee z′)$ I'm not supposed to use tables but only proprieties like De Morgan ecc. EDIT: So I ...
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### Why can't AND and NOT be represented with only IMPLICATION?

Can someone please explain why I can't use only IMPLICATION to represent AND and NOT with proof as well? I know that I can represent OR simply by using IMPLICATION. Was thinking if I could find ...
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### Clarity on Boolean Algebra and Rings

I'm trying to wrap my head around Abstract Algebra, Boolean rings, and it's a little difficult. So I understand the ring (I believe it's a ring) <ℤ ,x, +, -, 0, 1 > is normal integer arithmetic ...
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### De Morgan's Law Operation order

I have the following boolean logic: $$\overline {\overline {\overline {B+C+D} + \overline {DA}} + \overline {\overline {\overline {A+E} + \overline { B}} + \overline {E}}}$$ I am trying to simplify ...
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### Simplify semi-boolean expression

I'm trying to simplify the following expression: (A == B) OR ( (A > B) AND (A < C) ) Given that B <= C, this is my ...
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### How can I show a set B with 8 elements and two operations (huntington axioms)

How can I show a set B with 8 elements and two operations, such that the axioms of huntington for boolean algebra holds? I found it with set of 2 elemtnts. but can't understand how to start with 8 ...
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### Trying to prove Equivalency using Boolean Algebra

The question presented was to use boolean algebra to show that XY’Z + X’Y’Z’ + XY’Z’ + X’YZ’ ≡ XYZ’ + XY’Z + XY’Z’ + XYZ’ I've tried using various laws of Boolean algebra, but the answer that I ...
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### Expression conversion using de Morgan's laws

I'm sorry strongly, because it's a very dummy question... I have an example in the algebra of logic. I need to convert an expression using the rules of de Morgan - replace by the conjunction of ...
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### self dual boolean function

How many self-dual Boolean functions of n variables are there?Please help me how to calculate such like problems. A Boolean function $f_1^D$ is said to be the dual of another Boolean function $f_1$...
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### XOR equation with multiplication arrangment

How can I move all the X to one side so the equation will become x=y XOR <somthing>... \begin{align} &2x \oplus y = x \end{align} ...
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### On boolean algebras as rings, modules and/or R-algebras

After trying to make sense of first order logic from an algebraic point of view I started to read about boolean algebras (similar to the explanations given here: wikipedia on boolean algebras. I also ...
### Difficulty understanding why $P \implies Q$ is equivalent to P only if Q.
I have difficulties understanding why $P \implies Q$ is equivalent to P only if Q. I do understand that in the statement "P only if Q", it means if $\lnot Q \implies \lnot P$". Regarding this ...