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
1
vote
1 answer

Simplify $(x'+y)'(x+y)'$ with boolean algebra

So I'm doing some homework and trying to simplify $(x'+y)'(x+y)'$. So far these are the steps I've completed, but I'm not 100% sure that they're appropriate. $(x'+y)'(x+y)' = (x'+y)'(x’y’)$ $(x'+y)'(x’y’) = (x’’+ y’)(x’y’)$ $(x’’+y’)(x’y’) =…
secondubly
  • 477
1
vote
2 answers

What am I missing about this Boolean expression expansion?

Sorry if this is too basic, but I am working through Boolean Algebra and Its Applications and do not understand this expansion in the author's example 5 in section 1-6: $$(A+X+Y)(A+B'+Y') \rightarrow (A+AX+B'X+XY'+AY+B'Y)$$ But where are $AB'$ and…
jds
  • 2,274
  • 3
  • 24
  • 35
1
vote
1 answer

If ¬ has a higher precedence than ∨, could one affirm "¬ (p ∨ r) ∨ r" <=> "¬ ((p ∨ r) ∨ r)"?

I'm currently in a disagreement with a colleague over how one should intrepret the precedence of the ¬ operator in boolean algebra, and I hope someone here may enlighten me. We both agree that the ¬ operator has a higher precedence than the ∨…
user1729422
  • 13
1
vote
1 answer

Finding Product-of-Maxterms Form

I need help to resolve this problem, i have the following boolean function: [(A.!C)+!(A.!C)].!(A.!B) The Truth table is: (please see this LINK TO wolframalpha for more detail) Then the Sum-of-Minterms Form is: A.B.C + A.B.!C + !A.B.C + !A.B.!C +…
Gaston Flores
  • 115
  • 1
  • 6
1
vote
1 answer

Boolean Algebra: making a proof assistance

So far i've tried all the identities my teacher gave us and keep getting stuck I have to prove that x'y' + y = x' + xy using boolean algebra identities
Brandon Jerz
  • 37
1
vote
2 answers

Boolean algebra, ABC'+AB'C'+A'BC' = (A+BC'+C)C', can anyone show it please

I was asked to prove the next formula - (A+BC'+C)C' = ABC'+AB'C'+A'BC' i need to show all the stages of the simplification, i have all of the rules/identities. i have tried many times and i did not make it, i always get something else thank you
adar
1
vote
2 answers

Boolean Algebra: Can this be simplified further?

AB+CD+A’BD+A’BC+AB’D+AB’C AB+CD+A’B(D+C)+AB’(D+C) CD+(AB+A'B(D+C)+AB’(D+C)) CD+(AB+B(D+C)+A(D+C)) CD+AB+(B(D+C)+A(D+C)) CD+AB+(A+B)(D+C) This is what I got, but I'm not sure if it's correct. It's as good as I can get it algebraically. Can it be…
Hamster
1
vote
1 answer

Simplifying from POS using boolean algeabra

I have a boolean function, f expressed in the Product of Sum form. $$f = (A+B+C)\cdot(A+B+ \overline C)\cdot(\overline A + \overline B + \overline C) $$ On simplification I get, $$ f = ((A+B) + (C \cdot\overline C))\cdot (\overline A + \overline B…
Prasanth Ravi
  • 13
  • 3
1
vote
0 answers

What if I am not given the labels of a Karnaugh map?

Simplify this expression represented by the map $$\begin{matrix} 1 & 1 & 0 & 1\\ 0 & 0 & 0 & 0\\ 1 & 1 & 1 & 1\\ 1 & 1 & 0 & 1 \end{matrix}$$ With variables $a,b,c,d$. Should I be concerned I am not given the labels at the sides? I mean, can I…
Saturn
  • 7,191
1
vote
0 answers

Logical operations precedence and calculator program

I write the C library intended to be used in evaluating math expressions. It should support boolean algebra also. So at the moment I'm stuck with boolean precedence. I'm not a mathematician so that's my questions: 1) What is expected from a math…
pugnator
  • 111
  • 2
1
vote
1 answer

Simplify Boolean equations

I have simplified following Boolean expressions. Can somebody tell me whether they are right or wrong? 1) F1 = ~(~A ~B C + ~(AB)C) ~(~A ~B C) = ~(~A) + ~(~B) + ~C -------> Apply DeMorgan's law to the 1st term = A + B + ~C ---------> since A=~(~A)…
user156436
  • 11
  • 2
1
vote
1 answer

Simplying Boolean-Logic Expression

Can you help me simplify this or is this the simplified form? A = (X + Y + Z) (X + ~Y + ~Z) (~X + Y + ~Z) (~X + ~Y + Z) Here's my attempt: A = (X + Y + Z) (X + ~Y + ~Z) (~X + Y + ~Z) (~X + ~Y + Z) Using De Morgan's Law: ~ [A = (X + Y + Z) (X…
shriekyphantom
  • 11
1
vote
1 answer

Nand this Boolean Algebra Function?

I'm trying to convert this Expression that I got from minterms given to me by my professor to use only NANDS. I swear it should be right, but the output Multisim is giving me is false. minterms(0,1,2,3,4,5,7,14,15) Expression: ~A~B + ~A~C + ABC +…
Java Hopeful
  • 11
1
vote
2 answers

Proof of the identity of a Boolean equation $Y+X'Z+XY' = X+Y+Z$

How to prove the following the identity of a Boolean equation? $$ Y+X'Z+XY'=X+Y+Z $$ I have tried : $ \space\space\space\space\space …
Casper
  • 1,039
1 2 3
…
64 65