# 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.

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### Can you calculate the common volume on excel using Boolean Operation

I would like to calculate the common volume of a solid like the one below but at different angles. I can achieve this using ANSYS Design but I was wondering whether it is possible to calculate this on ...
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### Prove that with n variables there are 2^2^n possible boolean functions

I have tried looking it up on the Internet; however, most of the results did not make sense to me. I know that the statement is true, but how do you mathematically prove it? For reference the proof ...
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### What is the logical expression of undecidability? [closed]

undecidability = not false and not true = not (false or true) decidability = false or true then can true and false coexist? and, if we express undecidability of true or false in logic, ...
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### Parameter activity in boolean expression

As a Continuation to my first question I have found a way for determining the activity of each parameter. Activity definition: activity of each parameter is its contribution to get the whole ...
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### What is activity of argument in boolean function and the norm of a function?

1) I having problem understanding the concepts of activity of specific variable of a boolean function. For instance if we are given F= (x1'x2)XOR(x3 v x4')x5 ...
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### Proving $\|x=y\|\cdot \|\phi(x)\|\le\|\phi(y)\|$ in Boolean valued models

This question relates to the Boolean algebra approach to forcing. Fix a complete Boolean algebra $B$. I'm writing $\|\sigma\|$ for the Boolean value of $\sigma$, where $\sigma$ is a sentence of the ...
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### Number of self dual functions and number of inputs for which self dual function is 1

I came across this slides which states following two theorems: Theorem There are $2^{2^{n-1}}$ different self-dual functions of $n$ variables. Theorem Let $f$ be a self-dual function of $n$ ...
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### Polynomial size Boolean circuit for counting number of bits

Given a natural number $n \geq 1$, I am looking for a Boolean circuit over $2n$ variables, $\varphi(x_1, y_1, \dots, x_n, y_n)$, such that the output is true if and only if the assignment that makes ...
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### Proof of Demorgan's theorem by Principle of Duality. Is it valid?

I chanced upon a seemingly "too good to be true" proof of Demorgan's theorem for boolean algebra, however I'm not quite sure if it's valid. The principle of duality states that for a boolean algebra, ...
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### Proving the identity: (A\B) ∪ (B\C) = (A∪B) \ (B∩C)

Trying to prove the following identity: (A\B) ∪ (B\C) = (A∪B) \ (B∩C) I worked algebraically on the expression on the left and reached: (A\B) ∪ (B\C) = (A∩B') ∪ (B ∩ C') = ((A∩B') ∪ B) ∩ ((A∩B') ∪...
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### Boolean functions question

I am trying to solve exercise 1.29(a) from Ryan ODonell's Analysis of Boolean Functions which says that given $f:\mathbb{F}_{2}^{n} \rightarrow\{-1,1\}$ such that $dist(f,\chi_{S^{*}})=\delta$ for ...
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### finding essential prime implicants

F(w,x,y,z)=Σ(0,1,2,4,5,6,7,10,15) which one is correct, or both wrong. i'm confused about finding prime implicants at top right and bottom right