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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How to prove this equality?

I would like to prove the following using boolean algebra and not karnaugh maps but I'm stuck: CD' + CDAB' + C'D'AB' = CD' + CAB' + D'AB'
Sleeper
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2 answers

How to proof tautology without truth table in this case?

Hej, i got stucked while finding a solution to proof the following is a tautology. Can someone help me out please with a good tip? Thanks in advance
radscheit
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Simplifying Boolean Algebra law

I've got a problem here that I could use help solving. I have simplified it to this point. Using Wolfram Alpha, I know it is still possible. My lecturer did it but I didn't catch all of it. It is frustrating me like mad and I didn't want to come…
Pejman Poh
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2 answers

Prove that A’C + A’B + BC equals C (A XOR B)’ + A’B

Prove $$A’C + A’B + BC = C (A \oplus B)’ + A’B$$ Here is what i have tried: $$A’C + A’B + BC = C(A’+B) + A’B$$ Now, need to prove $(A \oplus B)’ = A’+B$ $$(A \oplus B)’ = A'B'+AB = \text{now what??}$$
Debanjan Dhar
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NOT and NAND Logic gate

My working .Z passes though NAND becoming Z' .Y passes through NOT gate becoming Y' .Y' Passes though NAND becoming Y therefore answer is Z'Y
DanS
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1 answer

Find the simplest form of this boolean function $[x+(xy)]·[x + (x'y)]$

$$ [x+(xy)]·[x + (x'y)]$$ My current belief is that it would be $0$ or $1$ but please correct me if I'm wrong
DanS
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if $a'b+cd'=0$, then prove that $ab+c'(a'+d')=ab+bd+b'd'+a'c'd$

Let $a'b+cd'=0$, then prove that $$ab+c'(a'+d')=ab+bd+b'd'+a'c'd$$ I would like to know how to solve this expression, not able to make any headway. I have tried canonical form expansion and reduction but the terms in the if condition does not match…
harindra bhati
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3 answers

Boolean Algebra Proof for a + a = a and (a * b)' = a' + b'

Prove, for any element $a$ in a boolean algebra expression, that $a + a = a$. Prove also, for any two elements, $a$ and $b$, of a boolean algebra expression, that $(a * b)' = a' + b'$.
SWAPAN KUMAR DAS
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Boolean Algebra Simplification Question --

I got some homework for Boolean Simplification, could someone please help me and solve this because I'm literally going to rip my head apart :D I've tried this multiple times but I keep ending up doing it wrong... A'BC'D'+ AB'C'D' + AB'CD' + ABC'D +…
Andrius Zapolskis
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2 answers

How can i apply Absorption law in this expression?

I have this expression: A + A * B * C' I know that i can use the Absorption law in this and the answer is A, but how can i apply that? Thank you.
ItzMeN0n
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1 answer

De Morgan's Law Operation order

I have the following boolean logic: $$ \overline {\overline {\overline {B+C+D} + \overline {DA}} + \overline {\overline {\overline {A+E} + \overline { B}} + \overline {E}}} $$ I am trying to simplify the logic, what confuses me is why I cannot apply…
user348525
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1 answer

How can i simplyfy this boolean equation?

Please help me simplify this formula by using boolean algebra rules: $F= x_1'x_2'x_3'x_4'+x_1'x_2'x_3x_4+x_1'x_2x_3'x_4'+x_1'x_2x_3x_4'+x_1x_2'x_3x_4.$ I know that the answer should be: $(x_1'x_3'x_4')+(x_1'x_2x_4')+(x_2'x_3x_4)$ from Karnaugh map.…
rauno45
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3 answers

Boolean simplification A'B'C' + A'BC + ABC'

Gentlemen I need a hint to simply this expression since I'm quite rusty in my boolean algebra. A'B'C' + A'BC + ABC' I however have made thus far A'B'C'+ B(A'C+AC') A'B'C'+ B( AA' + CC' + A'C +AC') //SUBSTITUTE FOR 2 ZEROS A'B'C'+ B( A(A'+C')+…
Desper
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4 answers

boolean algebra simple question

Simplfy : $$ (x+y)\cdot(x+yz) $$ I have tried to solve the question through by evaluating the expressions $x(x+y)$ and $yz(x+y)$ but I didn't get the right answer which is: $$ (x+y)\cdot(x+yz)=x + yz $$
Razi Awad
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1 answer

Do 'sum-of-products' and 'product-of-sums' represent the same function?

Do 'sum-of-products' and 'product-of-sums' represent the same function? Does it have be the same expression or not? In case it is different, what does it mean? Context: I've just made a Karnaugh map and the sum of products give me the same function…
Diego Vega
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