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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 .

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Convert boolean expression to pos then nor only

I'm trying to convert a + xb + xyz to POS then to nor only. First I got, a'(x' + b')(x' + y' + z') by using the duality rule but then I get confused after that. Thanks.
user252836
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Proof of the following statement?

For one of the inclass problems, we had to prove the following statment using Properties of Boolean Algebra: xyz + x'y'z + x'yz + xyz' + x'y'z' = xy + yz + x'y' My professor first grouped the terms on the left hand so Complement Rule can be used: =…
Jenna Maiz
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Boolean Algebra Simplification

Can someone show me the steps of simplification for this Boolean expression? (!A!B!CD) + (!AB!C!D) + (!AB!CD) + (!ABCD) + (A!B!CD) + (ABCD)
Riley
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Does $x(y+z)$ simplify to two variables in Boolean Algebra?

Question from the title. I'm just starting with Boolean algebra and my first set of exercises contains multiple problems which simplify to a variant of this. Am I "done" these problems, or can I still simplify further?
Mike Dumycz
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Is it possible to check if this function is associative without checking all the cases?

Given a boolean function with the following table: $$\begin{matrix} {A}&{B}&{out}\\ {0}&{0}&{0}\\ {0}&{1}&{0}\\ {1}&{0}&{1}\\ {1}&{1}&{0} \end{matrix}$$ Is it possible to check if it's associative or not without checking all the cases?
Red Banana
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Find the numbers by XoR

I have 6 numbers M1, M2 and M3 and E1, E2 and E3 such that M1 xor M2 = E1 xor E2 M2 xor M3 = E2 xor E3 M3 xor M1 = E3 xor E1 If M1, M2 and M3 are not equal to E1, E2 and E3 respectively, then given M1, M2 and M3 is it possible to find E1…
letshack
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Triple XoR - Find relation between the numbers.

I have a = b^c; b = a^c; Is it possible to eliminate c and find a relation between a and b? I have 3 different a values and would like to find the values of corresponding b. Thanks!
letshack
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a bit complicated boolean simplification

I'm trying to simplify the following boolean expression: [(A' (C+D)')'] (A) + ( B (DC) + (D'C') + A + CB' What I got is A + (C+D) + B [(DC) + (D'C')] + A + CB' A(A+C) + D + B[1] + A +CD' A + D + B + A +CD' (used absoprtion law for A(A+C) A + B + D…
williams
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Boolean Algebra simplify

The question is to simplify $$xy'z+wxy'z'+wxy+w'x'y'z'+w'x'yz'$$ Using K-map, the answer is $wx + w'x'z' + xy'z$ However, the question wants me to simplify algebraically, stating laws beside. I tried it for hours but it's just so hard I can't do it…
SMLJ
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If the following statements in which a, b, c,d are involved are simultaneously true, find the values of a-d

Can you please help me solve this ? This exercise says that we have the following statements: $$\lnot a \rightarrow b\tag{1}$$ $$\lnot a \Leftrightarrow c\tag{2}$$ $$\lnot b \rightarrow d\tag {3}$$ $$\lnot a \rightarrow d\tag {4}$$ $$ \lnot…
wonderingdev
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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 operations suggests an unintelligent error that it is…
Squirtle
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A question about truth tables

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 1001 so B' just needs to be 0 and D = 1 ? and on…
Pantelis10
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Stone space of finite Boolean algebras

Is the Stone space of every finite Boolean algebra a finite discrete space (for every finite Boolean algebra is complete, atomic, and isomorphic to the power set of its atoms; and finite discrete spaces are zero-dimensional, compact, and Hausdorff)?
user60264
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$f(x) = x$ or a , if $f(x)$ and $a$ is known find $x$ boolean algebra

I am new to boolean algebra. I am facing difficulty solving this problem: Given $f(x) = x \lor a$, for some $f(x)$ and $a$, deduce the value of $x$. Can someone provide me the solution with example? Similarly, if $p(x) = x \land a$ for some $p(x)$…
Deepak
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Boolean algebra proof and cancellation law

I have a Boolean algebra with some elements $a,b,c$. I have to show this: $(a ∧ b) ∨ (a′ ∧ c) ∨ (b ∧ c) = (a ∧ b) ∨ (a′ ∧ c)$. Now I have done other such proofs before but this one I got lost in. I see Boolean algebras have a cancellation law, so my…
Snowflake
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