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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What is the universe of a sub algebra generated by $\{(a \wedge b)\vee(c \wedge b') : a,c \in C\}$ ?

I need to prove the next thing, Let $B$ be a Boolean algebra and $C$ a proper subalgebra of $B$. Let $b ∈ B−C$. Prove that the set $\{(a \wedge b)\vee(c \wedge b') : a,c \in C\}$ is the universe of ...
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Distributivity of lattices and prime ideals.

I need help proving that, if $L$ is a lattice with the property that for every nonempty proper filter $F$ and every ideal $I$ such that $F \bigcap I = \emptyset$ then there is a prime filter $G$ such ...
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If a set X has the finite meet property, then there is an ultrafilter such that X is a subset of it.

I need to prove that if $X \subseteq B$ is a set with the finite meet property, then there exists an unltrafilter $U$ of $B$ such that $X \subseteq U$. I know that the finite meet property means that ...
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Does the class of all periodic subsets of $\mathbb{Z}$ of peroid greater than $k$ form a field of sets?

We say that a subset $X\subseteq \mathbb{Z}$ is a periodic subset of $\mathbb{Z}$ of period $k$ if the set obtained from $X$ by adding $k$ to each element of $X$ is $X$ itself. Does the class of all ...
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$p\implies q = p'\vee q$ and duality

I'm reading Halmos's Lectures on Boolean Algebras. The title is a definition and he then also defines $p\iff q= (p\implies q)\wedge (q\implies p)$. Then the following: The source of these ...
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Discrete Math Predicate Logic

Consider truth assignments involving only the propositional variables $x_0, x_1, x_2, x_3$ and $y_0, y_1, y_2, y_3$. Every such truth assignment gives a value of $1$ (representing true) or ...
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Set of Numbers when added in any combination always produce unique result

What I'm looking for is a set of numbers that when added in any combination they always have a unique sum? Is this called something? I have searched on google for hours and I'm having a hard time ...
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Hello guys i have a question, I am trying to make a truth table which consists out of 4 variables F(A,B,C,D) = B'D + A'D + BD Is it true on the truth table when for example in B'D we have 0001 or ...
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Boolean algebra Simplification of “xy + x'z + yz” [closed]

I'd like to simplify the following expression "xy + x'z + yz": ...
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How to convert a mod 2 function to an expression in Boolean Algebra

I'm not sure if this is the right place to post it but I have a question I'm having a hard time understanding. The questions is: Convert the function $X^3Y + 2XZ + WX + W$ mod $2$ to an expression ...
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Proof for $∃xA⇔¬∀x¬A$

I want to prove, that $∃xA⇔¬∀x¬A$, using classic axioms. I think, I have to start with the following step: $∃xA⇔∃x¬¬A$ But I do not know, how to make this step, using axioms: $∃x¬¬A⇔¬∀x¬A$
How to show that if $\neg b = a \land d$ then $a \land \neg b = \neg b$ and $b \land \neg a = \neg a$
I'm new to boolean algebra and am having trouble proving the following simple theorem. Many thanks for any help. If $\neg b = a \land d$ then $a \land \neg b = \neg b$ and $b \land \neg a = \neg a$. ...