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 my if conditions using Boolean Logic?

My code: def save_model(self, request, obj, form, change): if "_continue" in request.POST: if "PAN_ID" in request.POST and not change: try: data = Dematad.objects.filter( Q(PAN1=obj.PAN_ID)…
Vishesh Mangla
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Are boolean operations unique?

Are the well known operations of logic sum and logic product (defined by their two truth tables) the unique couple of operations (defined on a two elements set) that realize the axioms of: associativity, commutativity, absorption, identity,…
Antonio19932806
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Minimize Boolean function

I have got some silly task, but I am quite confused. Need to minimize function. $$f(x_1,x_2,x_3,x_4)=x_1x_2+x_1x_3+x_1x_4+x_2x_3+x_2x_4.$$ Thanks. Sorry for my English. Minimize Boolean function
0xDE4E15B
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Equivalent expression of $p' \cup (p\cap q')$

The proposition $p' \cup (p\cap q')$ is equivalent to $1.$ $p\cup q'$ $2.$ $p\to q'$ $3.$ $q\to p$ $4.$ $p\cap q'$? The given expression can be written as $(p'\cup p)\cap (p'\cup q')=1\cap (p'\cup q')=p'\cup q'$ How to proceed further?
aarbee
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How do I solve the following example using Kmap?

I am trying to solve the SOP function: Em(0,1,2,6,8,9,10). Here's what I got in the table: C'D' C'D CD CD' A'B' 1 1 0 1 A'B 0 0 0 1 AB 0 0 0 0 AB' 1 1 0 1 My output function is y = B'C'+A'CD'+AB'D'. Is it accurate? My…
Sakib Arifin
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How to simplify boolean function

How can I reduce the expression: $(A + B' + C)(A + B' + C') $ to $ \Rightarrow A + B' + C'$
Cody
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How to simplify boolean expressions.

I'm struggling to understand what rules to apply when simplifying boolean expression. For example: $$ B+(A\cdot(C+B) \overline C) $$ I'm not sure how to simplify this expression. Here is my attempt. $$ = B+AB\cdot(C+\overline C) \\ =…
redpd
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How to combine terms for a truth table containing two outputs

here's my truth table: A B C D Z1 Z2 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0…
The Random Movieman
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How to see that $(p\rightarrow q)\leftrightarrow(\lnot q\rightarrow\lnot p)$ is a tautology, without using truth table?

Consider: Statement-I: $(p\land\lnot q)\land(\lnot p\land q)$ is a fallacy. Statement-II: $(p\rightarrow q)\leftrightarrow(\lnot q\rightarrow\lnot p)$ is a tautology. Which of these statements is true? If both are true then is statement-II a…
aarbee
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Show that B is a Boolean subalgebra of $\mathbb{P(N)}$ which cannot be Boolean isomorphic to some $\mathbb{P(M)}$

Let $B = \{X \subseteq \mathbb{N} | X $ is finite or its complement $ \subseteq \mathbb{N}$ is finite$\}$. Show that B is a Boolean subalgebra of $\mathbb{P(N)}$ which cannot be Boolean isomorphic to some $\mathbb{P(M)}$.
rig
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Prove the following holds for all Boolean algebras?

For all x,y: (x ∨ y) ∧ x = x This is my attempt, I am just getting back to the question: (x ∨ y) ∧ x = x ∧ (x ∨ y) = (x ∧ x) ∨ (x ∧ y) = x ∨ (x ∧ y) = (x ∨ x) ∧ (x ∨ y) = x ∧ (x ∨ y) So where am I going wrong here?
weak_at_math
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Boolean Algebra with new definition

For two sets A,B with $B\subset A$ let us define: $$A-B:=A\setminus B $$ as the monotone difference. If $B$ is not a subset of $A$ then $A-B$ is not defined. Now my question. How to portray $A \cup B$ with only $-$ and $\cap$? Thanks for hints…
calculatormathematical
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Confusion in SOP and POS form

Given x’ + x(x + y’)(y + z’) Turn it into SOP and POS form (not the Canonical ones) and without using a K-map I have done as follows; = x’ + x(x + y’)(y + z’) = x’ + (x + xy’)(y+z’) = x’ + xy’z’+ xyy’ + xz’ + xy = x’ + xy’z’ + xz’ +…
Tyro
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How to prove that $A \Rightarrow (B \vee C) \equiv (A \Rightarrow B) \vee (A \Rightarrow C)$ using laws of logic

This question is something that I've tried to solve on my own, but with no such luck. The only thing I've managed to do using laws of logic is using contrapositive, then DeMorgan's Laws, and other laws that lead me to $(B \wedge A) \wedge (\neg C…
Daniel Jimenez
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Need help with Boolean alg

There's a Boolean algebra which happens: For any $y\in B$, if $y+y'=0$ then $y=0$ We need to Refute or prove
jezpack jezpack
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