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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boolean algebra minterm and maxterm expansion

I have an expression I'm not sure if i got right. The expression is $$ f(a,b,c) = a(b + c') $$ what i did was multiplied them out and added missing variables. which gave me $$ abc + abc' + ac'b + ac'b' $$ I'm sure there is something wrong I need…
user484263
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Prove 2 Boolean expressions are equal by multiplying out and simplifying

I was asked to prove that the following is TRUE by "multiplying it out" and simplifying: $(A+BC)(A+DE)=A+BCDE$ I am already familiar with the theorem $A+BC=(A+B)(A+C)$ which would be enough proof to prove this true in standard environments, but I…
wad11656
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Boolean algebra rules

I'm starting to learn Boolean algebra in the university, but I'm having difficulties trying to fully understand some rules. 1) If this expression “$A\Rightarrow B$” which is the same as saying as “$\lnot A \lor B$”, right? So take a look at this…
Pedro Diniz Gonalves Tavares G
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Simplify boolean expression to minimum number of literals

Problem is to simplify this boolean expression: $(a+b+c')(a'b'+c)$ I expanded it out and simplified to get to $a'b'c' + c(a+b)$ but that doesn't reduce the number of literals. Tried everything I could think of but I must be missing something...
lordgankoo
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Construct a formula, which satisfies two identities

I need to construct $A$, such that: $(r \rightarrow A ) \equiv(r \rightarrow (p \land q))$ and $(A \rightarrow r) \equiv(\lnot (p \lor q) \rightarrow r)$ I did some simple resolution steps to simplify identities: $( \lnot r \lor A ) \equiv( \lnot r…
Ladenkov Vladislav
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Simplify $ABC+A'BC+AB'C+A'B'C'$ to logic gates

I've simplified $ABC+A'BC+AB'C+A'B'C'$ to $BC+AC+A'B'C'$. However, I want to go further to logic gates for which ICs are readily available. I would like to use at most three such ICs.
umair mughal
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Simplify X = A(AB)' + A'B'C + ABC

Why is this way of simplifying the Boolean expression wrong? X = A(AB)' + A'B'C + ABC = A(AB)' + C(A'B'+AB) //A'+A = 1 = A(AB)' + C = A(A'+B')+ C = (AA')+AB'+ C = AB'+ C Is it wrong because C(A'B'+AB) ≠ C(1)? Can someone explain to me…
BEX
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Simplifying boolean function using boolean algebra

How to simplify the following expression : A'BCD + AB'CD' + AB'CD + ABC'D + ABCD' + ABCD ? It should get AC + BCD + ABD using Kmap but using boolean algebra i am stuck no matter how i try .
Dina
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Give all Boolean algebras on the finite set

Given a finite set $X=\{1,2,3\}$, are the following all the Boolean algebras? $A_1=\{\{1\},\{2\}\},$…
Jay
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Universality of $a{\wedge\neg}b$ gate and similar

According to the Wikipedia and other sources only NAND/NOR make one-element sets that are functionally complete. Then, there are also a lot of two-element functional complete sets. Question: why $a{\wedge\neg}b$ (and similarly ${\neg}a{\wedge}b$ and…
artemonster
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How to get a largest subset where the xor operation between the elements of that subset is equal to k?

A List and k are given inputs Let's take list [1, 2, 3, 4, 5] so the subsets obtained by XORing equal to k => 7 are {2, 5}, {1, 2, 4}, and {3, 4}. I want to print {1, 2, 4} where this subset count is largest among all other subsets. one more…
Raghavendra Temkar
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Simplifying Boolean Function with Karnaugh Maps

Given the boolean function f(x,y,z) = xyz + xyz' + xy'z + xy'z' + x'yz + x'y'z + x'y'z' (where x' = not x) In a three variable Karnaugh Map: yz yz' y'z' y'z x 1 1 1 1 x' 1 1 1 The goal is to group the adjacent units…
user1234440
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Complex Boolean simplification

Simplify the following Boolean expression: $$F=A'B'C'+A'B'C+A'BC'+AB'C'+AB'C.$$ I have tried and am getting stuck at $A'+B'+C'+A'BC'$. According to the K-Map it should get to $B'+A'C'$.
Seffu
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If X is a subset of a complete boolean algebra, must there be a finite $Y \subset X$ s.t. sup(Y) = sup(X)?

The question came up when I was trying to prove the compactness of the stone space S(B) of a complete boolean algebra B. Using only the basic facts regarding ultrafilters and boolean algebras, I cannot seem to find an answer. Thank you very much, in…
John Toh
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Simplifying a Boolean expression (confused)

Could somebody help me make sense of how to use the Boolean rules to simplify this expression? $$(x'+(yz)')(x + z')'$$ I used distributivity to get $$(x'+y')(x'+z')(x'+z)$$ I don't know if that was the right path to go down, or where to go from…
user433367
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