# 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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### General rules for transforming boolean equations?

Are there general or restricted rules for transforming between equivalent boolean equations? A concrete problem that I have is given the following equation: ...
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### Help with Simplifying boolean algebra, not sure if i have done it correctly.

I have no idea how to do boolean algebra, First question is x'y + x(x + y') I need to first draw a circuit diagram(logic gate) and then simplify it and draw a simplified logic gate. As of now I ...
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### Deriving minimal SOP forms from Karnaugh maps

Given the following picture, I have derived that the list of all prime implicants are a’c’d’, a’bd’, acd, ab’ and all essential prime implicants are also a’c’d’, a’bd’, acd, ab’. But I am not sure how ...
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### Do associative laws holds for XOR (exclusive or) and | (sheffer stroke)? [closed]

How can I prove if it holds or not for those operators?
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### Consensus Theorem and Boolean algebra

I am trying to prove the following boolean equality. $$bc + abc + bcd + a’(d+c) = abc + a’c + a’d$$ I have simplified the left side to $bc + a'd + a'c$ by factoring out a $bc(1)$. However, ...
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### number of permutation in a boolean expression containing only ANDs and ORs

I need to find the number of permutations of some expression which contains only conjunctions and disjunctions e.g.: $$e = x_1x_2 \vee x_3x_4$$ where $x_1x_2$ and $x_3x_4$ are boolean summands, ...
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### boolean algebra with finite elements

I need to define a boolean algebra with 8 elements. I know all the Axioms to define a binary boolean algebra but I don't know how to do that with 8 elements. Someone can guide me please? Thanks.
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### Boolean algebra - Maxterms

I have a boolean expression and I need to get to its canonical forms (sum of minterms and product of maxterms). In order to get an expression for the first canonical form, I need to multiply every ...
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### Is there a name for a semiring in which both operations distribute over each other?

For a semiring over a set $S$, with the operations $+$ and $*$, along with respective units $0$ and $1$, we have the law: $(a + b) * c = (a * c) + (b * c)$ But there are some semirings in which the ...
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### Boolean Logic using proofs

ABC' + C = AB + C I understand this using venn diagrams and intuition. However, I am not able to derive the proof for getting from one side to the other. It's probably very simple step that I keep ...
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### Demonstrate AB+C(A+B)=AB+C(A⊕B)

Please help me demonstrate that AB+C(A+B)=AB+C(A'B+AB'). I've tried a couple of times but i always reach AB=2AB .
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### Ideal generated by a set of polynomials $X^{a/b}$ where each monomial having $a$ and not having $b$

Let $$\mathcal R=\mathbb Z_2[x_1,\dots,x_n]/\langle x_1^2-x_1,\dots,x_n^2-x_n\rangle.$$ I want to learn ideal arithmetics to deal with polynomials of the forms such as Consider a set of ...
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### Quick question on Bitwise operations

I have some questions for homework to do with Bitwise operations, now it's a simple task but it doesn't actually explain how to handle the questions which is why I'm asking here before I begin ...
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### Simplify $AC'+A'C+BCD'=AC'+A'C+ABD'$

How to prove that $$AC'+A'C+BCD'=AC'+A'C+ABD'$$ approch: a way to demonstrate is expressed in its canonical form. Any hint would be appreciated.
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### How can I show a set B with 8 elements and two operations, such that the axioms of huntington for boolean algebra holds?

If It was about two members I would have choose B={0,1} with the operations: AND , OR And prove this. But how can I do this with 8 elements?
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### Boolean algebra; what does <-> mean?

Expression :$$(p\rightarrow q)\leftrightarrow(\neg q\rightarrow \neg p)$$ What does the symbol $\leftrightarrow$ mean ? Please explain by drawing the truth table for this expression and also with ...
Suppose I have a Boolean function $f:\mathbb{F}_2^n\rightarrow \mathbb{F}_2$ which satisfies the following property: $$d(f, \ell)\leq 2^{n-1}\quad\forall\; \text{linear functions}\; \ell .$$ where ...