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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Prove that NAND and NOR are the only Universal Logic Gates.

I was watching this lecture: link H(x,y) is a boolean function. He's says that H(x,y) is a Universal logic gate if and only if H(x,x) is 1 - x. I didn't get this part. So how to prove that NAND and NOR are the only Universal Logic Gates ?
Het
  • 333
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How would you simplify the following boolean expression $(!A B)+(B !C)+(BC)+(A !B !C)$?

How would you simplify the following boolean expression $(!A B)+(B !C)+(BC)+(A !B !C)$? I factorised B and managed to get $B(!A+!C+C)+(A !B !C) = B+(A !B !C)$, but I do not know how to continue. Using a K-map, I managed to get the result of $B+A!C$…
user792841
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Simplify a boolean algebra expression to switch between values

I'm a little rusty on my boolean algebra and am looking for some help. I need to select between two values (Y & Z), based on the value of X. If X is true, W should be equal to the value of Y. If X is false, W should be equal to the value of Z. …
DrTarr
  • 161
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I need to write this expression in Kmap but I dont how to write '(A+C) correctly

I have to do synthesis of combinational logic circuit from this expression first I have to do K map (karnaugh) and I want to know how can I correctly do it. The expression is (A+'B)('C+D)'(A+C) Tip: A+C is in complement.
user730768
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3 answers

Boolean algebra: simplify (A+B)$'C'$(C+D)

I need to solve / simplify the output of a logic circuit. The output is $(A+B)'C'(C+D)$ I wrote the truth table and it returns 0 in all outputs. I tried to solve it using laws of boolean algebra: $(A+B)' = A'B'$ And $C′(C+D) = (C′C + C′D)$ $C′C = 0$…
Sakib Arifin
  • 151
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Boolean algebra equation: ABC OR A'B'C'

I have also tried with K-map but i get a different result: CD |00 | 01 | 11 | 10| +------------------ AB 00| 1 | 0 | 0 | 0| --+---+----+----+---- 01| 0 | 0 | 0 | 0| --+---+----+----+---- 11| 1 | 1 | 1 | 1| …
Dragos Makovei
  • 25
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Boolean algebra problem simplification

I am trying to simplify the following Boolean expression $$xz + x'y + zy$$ and the solution said it was $xz + x'y$. How did they get this answer? Also, I found this on the MIT site.
Adil Ali
  • 59
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What is the most efficient way to check if x or x bar as more ones?

For example, taking the number x=74, which in boolean is 1001010 . I denote x_bar as x_bar= 0110101. Here we see that x_bar has more ones.
Aayush Soni
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AB+B((B+C')+B'C) can be simplified to

The answer is B+C but When I tried to solve I got a different answer, which is B. The way I solved AB+B((B+C')+B'C) =AB+B(B+C')+BB'C =AB+BB+BC'+BB'C =(BB'C=0,BB=B) then AB+B+BC' Taking B out frm all terms B(A+1+C') =B [A+1+C'=1] What is the…
Abhijith
  • 21
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Is this a finite Boolean algebra?

Suppose in a Boolean algebra that the finite sum of all the atoms gives $1$. Does it follow that this Boolean algebra is finite? I was motivated by the following: Does there exist an infnite Boolean algebra with only one atom?
Squirtle
  • 6,698
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Boolean algebra: Why does the equation hold?

I want to show that $$\bar y\land (x\lor z)\land (\bar x \lor \bar y) = \bar y\land (x\lor z)$$ I have done the following: \begin{align*}\bar y\land (x\lor z)\land (\bar x \lor \bar y) &=\bar y\land \left [(x\lor z)\land (\bar x \lor \bar…
Mary Star
  • 13,956
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Proving both distributive laws for Boolean algebra given by certain axioms.

In the book "Introduction to mathematical logic", Elliott Mendelson gives the following axiomatization of Boolean algebra: We call the triple $(B,\cap,')$ a Boolean algebra whenever $B$ has at least two elements, $\cap$ (meet) is two-argument…
Kulisty
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How do we know what $A$ or $B$ or $C$ is after simplifying?

I understand the basics of boolean algebra and how to simplify them. What I am confused about is how do we know what to call a value after simplifying? Imagine we create a boolean algebra expression in canonical form. When simplifying we come across…
MegaWitt
  • 25
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Given a Boolean function, decide if it can be implemented only with the $\mathrm{AND}$, $\mathrm{OR}$, and $\mathrm{NOT}$ gates

True or false? Prove or justify, respectively. "Given $$f(x,y,z)=x\cdot z+\overline y\cdot\overline{z+\overline x}$$ can be implemented in a circuit formed only by an $\mathrm{AND}$ gate, an $\mathrm{OR}$ and a $\mathrm{NOT}$". I think it is…
manooooh
  • 2,269
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Incompleteness of Connectives

I’m currently trying to learn more about Mathematical Logic and have reached a sticking point. I also have the solutions to the problems I’m working through and I usually don’t need to ask for help to understand a concept, but this problem is still…
Amateur Math Guy
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