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 .

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Why Is The Number of Boolean Subfunctions Based on a Min and Not a Product?

In Stasys Jukna's book "Boolean Function Complexity", he states that for an n variable Boolean function, the number of distinct subfunctions on $Y$ variables (meaning $Y$ variables have not been assigned to constants), is the minimum of $2^{n-|Y|}$…
ian.p.swift
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Reduction of any Boolean function to disjunctive normal form.

How can any Boolean function be reduced to disjunctive normal form ? With examples it's clear, but can anyone help me with a general proof ? Thanks in advance.
math
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$D_{m}$ is a boolean algebra iff there is no prime $p$ such that $p^2 \mid m$

$D_{m}$ is a boolean algebra iff there is no prime $p$ such that $p^2 \mid m.$ How can I prove this? Could anyone help me please?
user591668
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Simplifying a boolean expression with four inputs using boolean algebra

The expression I need help simplyfing is: $\lnot$ A$\lnot$B$\lnot$C$\lnot$D + A$\lnot$B$\lnot$C + A$\lnot$BC$\lnot$D + ABD + $\lnot$A$\lnot$BC$\lnot$D + B$\lnot$CD + $\lnot$A which can be simplified into: $\lnot$A + BD + $\lnot$B$\lnot$C +…
usernamn
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Boolean Expression Orders of Operation

Using DeMorgan's Law, write an expression for the complement of F if F(w, x, y, z) = xyz'(y'z + x)' + (w'yz + x') F' = (xyz'(y'z + x)' + (w'yz + x'))' = (xyz'(y'z + x)')' * (w'yz + x')' = ( (xyz')' + (y'z + x) ) * ( (w'yz)' * x ) = ( ( (xy)' + z )…
Hemofelicity
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Simplification - Boolean Algebra using DeMorgan law

Can somebody please help me simplify this expression using DeMorgan law. $\lnot{(A\land B)}+\lnot{(\lnot{A}\land B)}$ Thank you.
John
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Boolean Expression x'y + x(x + y')

I'm still learning Boolean Algebra so I apologise if the question seems pretty straight forward. After working on this problem I thought the answer was 'x', my working out was: x'y + x(x + y') = x'y + xx + xy' = x'y + x + xy' = x + xy' = x but…
HKeys34
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Simplifying x'y'+y'z+xz+xy+yz'

Someone help me to simplify this boolean expression. $x'y'+y'z+xz+xy+yz'$ I understand the laws used but still not getting the exact answer. I would appreciate if someone solved this for me. My attempt so far: $$x'y'+y'z+xz+xy+yz'=…
Ganchimeg
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Difference between Boolean formula and Boolean expression

I have read in a book here something I think is wrong. It says that a boolean function $\phi:B^2\rightarrow B$ defined by a truth table where {0,1} and {0,0} returns {1}, cannot be expressed with a boolean expression of two variables $\phi(x,y)$. I…
Izar Urdin
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Trouble understanding boolean logic proof.

*Find the complement of $F=x+yz$; then show that $FF’ = 0$ and $F + F’ = 1$ $F(x,y) = x+yz$ $F’(x,y) = (x+yz)’ = x’(yz)’ = x’(y’+z’)$ $FF’ = (x+yz)x’(y’+z’) = (xx’+x’yz)(y’+z’) = x’yz(y’+z’) = x’yy’z+x’yzz’ = 0+0 = 0$ $F+F'=…
Ishmael
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Software to Find Kernels/Co-Kernels of Boolean Expressions

Is there any (free) software available that calculates all the possible kernel/co-kernel pairs of a boolean expression?
John Roberts
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LC-3 instruction set. Help needed

Using only one LC-3 instruction, how would I move the value in Register 2 into Register 3 How to perform R1 = R2 - R3 using only 3 LC-3 instructions? Hope you can help. Thanks
Greeny Ghuji
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Memory and bits

If a memory's addressability is 64 bits. What does that tell you about the size of the memory address register (MAR) and memory data register (MDR)?
Greeny Ghuji
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I can't simplify this A’B’C + A’BC + A’BC’ + AB’C + ABC boolean expression to A'B+C

I have to get this expression A’B’C + A’BC + A’BC’ + AB’C + ABC to A'B+C. I did this but I can't finish it, I don't know how to. A’B’C + A’BC + A’BC’ + AB’C + ABC A'B(C+C')+C(A'B'+AB'+AB) A'B+C(A'B'+AB'+AB) That's it, I don't know how to solve that.
Mica B
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Boolean Algebra with and without top

In Wikipedia, the Boolean algebra is defined as a 6-tuple $(A,\wedge,\vee,\neg,0,1)$. In Kuratowski1976, on the other side in the definition on page 34, there is no $1$. Halmos1963 has the $1$. Does the definition in Kuratowski1976 leads to…
Mohamed Ali
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