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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Element chasing style proof applied to Boolean algebra problem

I would like to apply an element chasing style proof to the following problem: Let $P$, $Q$ and $R$ be elements of a Boolean algebra. Prove that if $$ \tag 1 P + Q = P + R$$ and $$\tag 2 P \cdot Q = P \cdot R $$ then $$\tag 3 Q = R$$ Given (1)…
bosra
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Explanation needed on rules for boolean simplification

Good day I am getting confused on Boolean function simplification. I dont quite understand how the equation is simplified as in the rules for simplification in boolean algebra. Can anyone help explain how i would simplify these two examples. AB'C…
Geo
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Simplifying the boolean expression for leap year

Suppose I have p = year divisible by 4 q = year divisible by 100 r = year divisible by 400 and by constructing the truth table I get p | q | r | is_leap_year ---+---+---+-------------- 0 | * | * | 0 1 | 0 | 0 | 1 1 | 0 | 1 | 0 1 | 1 | 0 | 0 1…
Jeffrey04
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What is this boolean algebra expression inverted?

I basically have this boolean algebra expression: ((xDir === 1 || xDir === -1) && (yDir === 1 || yDir === -1)) What is the "inverse" of this? I tried using DeMorgan's thereoms but I don't think I did it properly. I ended up with something…
pizzae
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Boolean simpliication problem

Question My answer I stuck in the middle. How to simplify it further
Tortoise
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Boolean Algebra Simplification Help, Need AND's, OR's, NOT's only

I'm having a very hard time simplifying this: A!B!C+ABC+!A!BC+!AB!C The objective here is to simplify the equation until it can be expressed in "AND"'s "OR"'s and "NOT"'s. I have to create an integrated circuit for the simplified expression using…
edwin
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simplification in boolean algebra

Please could someone help me understand how; A + ~AB = A+B Actually, I don't understand how from A + ~AB we arrive at A+B Anyways thanks for helping me in advance!
Grammy
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Prove $x' + y' + xyz' = x' + y' + z'$

I had this question in an exam this morning but was unable to solve it. How would I start approaching this proof? I've tried multiplying x by ($y+y'$) or ($z + z'$) and similarly with y, multiplying it by ($x+x'$) or ($z+z′$) and gotten stuck. For…
Broadsword93
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How can bitwise operations be modeled with math?

In programming, if I did 100 | 001 (| being the "or" operator), I would get 101. Can this be done in math? I.e. with sets: $$A=\{1,0,0\}$$ $$B=\{0,0,1\}$$ $$A ?B = \{1,0,1\}$$ Is there an operator that would satisfy the equation in place of the…
Archie Gertsman
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Is this boolean algebra problem solvable?

My professor is of no help at all. He's foreign and is giving assignments that are written poorly, and is teaching stuff far beyond what he's supposed to be teaching at this level. Nonetheless, he's given this as a problem on an assignment and I'm…
Mirrana
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Prove the equivalence between two logical functions

I'd like to find out the equivalence existing between these two logical functions, I was trying it just by applying Boole's theorems in just one of them, but still have not arrived to a conclusion yet. $$\overline{ab}h + \overline{c}fgh +…
edusola93
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Express without sum or multiplication (Boolean algebra)

I'd like to express $AB$ just in terms of sum, I have already tried this: $(A′B+AB′)′\cdot(A+B)=AB$, but, of course, $A'B$, for example, is still multiplying. And also, I'd like to do the reverse process, expressing $ab + a'(b+c)$ just in terms of…
edusola93
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In boolean algebra, having trouble reducing (¬a∨b)∧(¬b∨a).

Starting with (¬a∨b)∧(¬b∨a), I'm having trouble reducing this to: (a∨b)⟹(a∧b) I am lost with what is the next step after (¬a∨b)∧(¬b∨a). Is it this perhaps?: ¬(¬a∨b)∧¬(¬b∨a) ? And then work on from there?
Ivan Lendl
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Reducing a boolean expression to XOR gates.

Is there any method or recommendation to reduce a boolean AND, OR expression to a XOR expression? For example I can reduce the following expression like this: $$\bar{A} \bar{C}+\bar{A}B+BC = \overline{(A \oplus C)(B \oplus C)}$$ Requires moderate…
Desty
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Can a Case Function Take Logical Expression? Or, Can I Call It a Boolean/Logical Case Function?

$P$ and $P'$ are strings (sequence of characters). $P_i$ and $P_i'$ are characters. I want to define equality condition between $P$ and $P'$ like the following: $Equal(P,P')=\begin{cases} \mathrm{false}, & |P| \neq |P'|…
GyuHyeon Choi
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