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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Simplification of: A’(BC + AB + BA’) in boolean algebra

I am trying to understand the simplification of the boolean expression: A’(BC + AB + BA’) I was wondering if someone could show me the steps needed to do this. Thank you in advance
dobdobeh alias
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Simplification of: AB’ + BC + C’A in boolean algebra

I am trying to understand the simplification of the boolean expression: AB’ + BC + C’A I know it simplifies to A + BC And I understand why, but I cannot figure out how to perform the simplification through the expression using the boolean algebra…
dobdobeh alias
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Prove, not using truth table, that $a b+a^{\prime} b^{\prime}+b c=a b+a^{\prime} b^{\prime}+a^{\prime} c$

Question: Let $B\left(+, \cdot,^{\prime}\right)$ be a Boolean algebra and $a, b, c \in B$. Prove, not using truth table, that $a b+a^{\prime} b^{\prime}+b c=a b+a^{\prime} b^{\prime}+a^{\prime} c$. Sol: We have $a b+a^{\prime} b^{\prime}+b…
BSC
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How to prove these two boolean expressions are the same using boolean theorem?

Expression 1: $Y = B'C' + B'A' + A'C$. Expression 2: $Y = B'C' + A'C$. Both of the expressions generate the same truth table which implies they are the same. However, how do you demonstrate they are the same using just boolean theorem? If both…
Anastazia Nichole
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Solving a Boolean Algebra Simplification via Algebra

I have been trying to simplify a boolean algebra expression, ( B+AC)~(A+B~C)+(AB~C). Through thinking through it, and its truth table, I'm pretty sure the answer is (~A~B)+(AB~C). I monkeyed with the algebra and removed the big bars which seemed…
Hailrig
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How do we go about factorizing boolean expressions?

How do we know how to go about factorizing a boolean expression when there are so many ways? For example, the factorized form of $ABC + A'B'C'$ is $(A + C')(B' + C)(A' + B)$, but how do we know how to derive this result?
Pacerier
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How to simplify XYZD + X'P +Y'P + Z'P + D'P without demorgan law or without combining variables.

I have to simplify the following boolean expression by proceeding only in POS form and not combining variables: XYZD + X'P +Y'P + Z'P + D'P Notation is . means AND + means OR ' means NOT "." is omitted wherever unambiguous as AND has precedence…
Nishant
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Question on proving !A & B || A & !B = A XOR B

I do apologise if this question has been asked before, but I am having trouble trying to get from !A & B || A & !B to A XOR B. I've tried doing it in reverse by starting with A XOR B ((A || B) & !(A & B)), and I reached (A || B) & (!A || !B) and…
bbayu
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Demorgans theorem confusion

In demorgan's theorem we were taught on three steps to achieve the answer First step is to not all inputs If the given is $ab$ then $(a)'(b)'$ Second step is to change the sign opposite to the current sign. From or to and and vice…
Mendrix Manlangit
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Does a law for A in boolean algebra hold true for not A as well?

Okay, so according to associative law: (A + B + C) = (A + B) + C So, could I also assume that ~(A + B + C) = ~A + ~B + ~C = ~(A + B) + ~C Where "~" means NOT and "+" means OR. Thank you very much.
Threshold19
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Difficulty simplifying boolean algebra expression

I am simplifying a boolean algebra expression and so far my expression is $$xy + zy + !x*z$$ The answer sheet says the answer is $xy + !x*z$ and when i type in my expression into an online boolean logic calculator it shows the same answer, however i…
NixyCron
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Convert 3-sat to n-sat with same variables on each clause

How to convert 3-sat with $n$ variables, where each clause is having only two operators: OR and NOT, and all the clauses connected with AND operator. To n-sat where each clause has the same $n$ variables connected with OR and NOT operators, and all…
Ilya Gazman
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What does it mean by binary operation ( taking gcd and lcm )?

I'm less than a rookie so it might seem like an easy question but I want a head start to figure things later on my own. The question wants me to prove that the set $D(m) = \{ x \in \mathbb N - \{0\} : x\mid m \}$ where $m$ is a positive number, is a…
Omar Muhammed Aly
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Expressions Simplifications Boolean Algebra

Expressions Simplifications Boolean Algebra I started simplifying function and got to the detailed picture and wanted to know if I can reduce the above expressions, for example : Y'.X'.Y = 0 ? Y'.X'.Z.X = 0 ?
Ofir Attia
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Boolean Algebra Simplification Question - Proof of equation

Boolean Algebra Simplification Question - Proof of equation I`m trying to proof this equation: X'.Y' + Y'.Z + X.Z + X.Y + Y.Z' = X'.Y'+X.Z+Y.Z' What your are suggesting? to add some (Y'+Y) or (Z'+Z) Thanks. EDIT - SOLVED
Ofir Attia
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