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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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Equivalent condition of completeness of Boolean algebras

A Boolean algebra $\mathcal{B}:=(B,\leq,\lor,\land,^c,0,1)$ is said to be complete if every non-empty subset of $B$ has a greatest lower bound (g.l.b). Show that for $\mathcal{B}$ to be complete, it is necessary and sufficient that every non-empty…
stoic-santiago
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$h:\mathcal{B} \to \mathcal{B'}$ (onto) is an isomorphism iff $\forall x,y\in B$, $x\leq y$ iff $h(x)\leq h(y)$

Let $h: B\to B'$ be an onto map, where $\mathcal{B}:=(B,\leq,\lor,\land,^c,0,1)$ and $\mathcal{B'}:=(B',\leq,\lor,\land,^c,0,1)$ are Boolean algebras. Show that $h$ is an isomorphism from $\mathcal{B}$ to $\mathcal{B'}$ iff for all $x,y\in B$,…
stoic-santiago
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How an interval [a, b] in a Boolean algebra B can be made into a Boolean algebra?

How an interval $[a, b]$ in a Boolean algebra $B$ can be made into a Boolean algebra?
H.Sh
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Simplifying Boolean Logic Relation

Simplification of $X \ \ \overline{(\overline{X} Y + \overline{Y}Z)} +\overline{X}$ The answer found is $\overline{X}+Y+\overline{Z}$ I tried the following approach, but ends up in two term…
Aruha
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How to simplify the Boolean expression (A'B+C)'(C+A)?

I am trying to solve the following problem: (A'B+C)'(C+A) = (AB'+C')(C+A) = AB'C+AB'A+C'C+C'A = AB'C+AB'A+0+C'A = AB'C+AB'+C'A Than what?
Sakib Arifin
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How to simplify the following SOP expression in Boolean Algebra?

Can anyone help me with the following Boolean Algebra…
Utkarsh
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Boolean simplification to OR expression

I noticed that $$\bar{B}C + B\bar{C} + BC$$ is equivalent to $$B + C$$ but I wasn't sure how I could use boolean algebra to simplify this down. I think it has to do with factoring out a term to get $$(\bar{B} + B)$$ which then equals 1, but I'm not…
Evan
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How does it evaluate A XOR B XOR C?

I am trying to solve the following combination, A | B | Cin | Sum | Cout 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 …
user2857
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I can't find a way to simplify this boolean algebra

xyz' + x'y + x'z the answer from boolean expression calculator on the internet is x'z + yz' I know the end x'z same like the answer. but I can't find a way to simplify xyz' + x'y = yz'
mas bro
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Boolean expressions simplification

I have found these boolean expressions based on a truth table: $(abc'd') + (ab'c'd) + (a'bcd') + (a'b'cd)$ (EDITED for 2)) $(abcd') + (abc'd) + (ab'cd) + (ab'c'd') + (a'bcd) + (a'bc'd') + (a'b'c'd) + (a'b'cd')$ However, I need to simplify them.…
user759166
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How do you simplify a boolean algebra expression when it's a two by three expression?

I'm a little stuck in my simplifying of this boolean logic expression. If it was $2 \times 2$, I know I could foil, but I can't find any law that will help me go any further. Would someone help me figure out where to go now? In this attempt, $\cdot$…
Threshold19
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How to simplify the Boolean expression $A'BC + AB'C' + A'B'C' + AB'C + AB$?

How to simplify this Boolean expression? $$A'BC + AB'C' + A'B'C' + AB'C + AB$$ I have solved it using Kmap and found the answer to be $$A + BC + B'C'$$ I tried simplifying it using the rules but only got to $$B'C' + C (A'B + AB') + AB$$ Seeing…
pi3.14
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Does this Boolean system of equation correct in both reverse and forward implication?

I am not sure if this Boolean system is correct in both reverse and forward direction ? $\begin{gathered} \left\{ {\begin{array}{*{20}{l}} {a + b + c}& \equiv &1&{{\text{mod}}\;2}&{\;(1)} \\ {b + c + d}& \equiv &1&{{\text{mod}}\;2}&{\;(2)}…
Tuong Nguyen Minh
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Simplify $ab' + ( a'+b )c$

Boolean algebra How to solve it. I am stuck after first step which is $ab' +(ab')'c$. After that I couldn't get the exact answer. The answer is $ab' + c.$
Utkarsh Sharma
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Which of the following sets of boolean functions is functionally complete?

Let us have two sets of boolean functions: $F_1 = (M \setminus T_0) \cup (S \setminus L)$ $F_2 = (M \setminus T_0) \cup (L \setminus S)$ where $M$ is the set of all monotonic functions, $T_0$ is the set of all falsity-preserving functions, $S$ is…
Play4u
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