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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Using Boolean Algebra to prove k-map result

I have been stuck on a homework problem which asks first to simplify a boolean equation using a k-map and second to reach the same result using boolean algerbra. The k-map was no issue and I have verified the k-map result, but no matter what I do, I…
Seth Duke
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finding essential prime implicants

F(w,x,y,z)=Σ(0,1,2,4,5,6,7,10,15) which one is correct, or both wrong. i'm confused about finding prime implicants at top right and bottom right
samexmm
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using only two-input NOR gates to implement the following function

F(A,B,C,D)=(A⊕B)'(C⊕D) =(AB'+A'B)'(CD'+C'D) =(AB')'(A'B)'(CD'+C'D) =(A'+B)(A+B')(CD'+C'D) how to simplify further
samexmm
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Simplify the expression: $((XY+X')\oplus (Y+YZ))'$

Simplify the expression: $((XY+X')\oplus (Y+YZ))'$ I can go as far as: $$((XY+X')\oplus (Y+YZ))'$$ $$\text{I use the rule of absorption:}$$ $$((Y+X')\oplus Y)'$$ Now I see that if $Y=1$ than the result is one and if $Y=0$ the result is $X$, but…
asaf92
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NOR gate circuit product

For the following figure: what is the ouput if a) both inputs are low b) if one input is high and one low c) does the circuit act like an OR or AND gate I understand that the output for the first part of the circuit is 1 if both inputs are low…
julian
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All Boolean Laws?

Boolean Laws For Boolean Mathematics Annulment A + 1 = 1 A . 0 = 0 Identity A + 0 = A A . 1 = A Idempotent A + A = A A . A = A Double Negation A̅̅ = A Complement A + A̅ = 1 A . A̅ = 0 Commutative A + B = B + A A . B = B . A De…
Bachi Nirosh
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Boolean Theorems - Simplify Function

I am currently taking a Discrete Mathematics course, along with Intro to Hardware course. I am having issues wrapping my head around Boolean Theorems, simplifying functions given to smaller circuit design. One problem that I am working on at the…
Kei U.
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Show that $x \wedge y = x \iff x \vee y= y$ using the following properties

Suppose $L$ is a set with binary operations $\wedge$ and $\vee$, along with the special $T$ and $F$ (for an $x,y,z \in L$) such that the following rules hold: $x\wedge T=x$; $x\vee y=T$ $x\wedge F=F$; $x\vee F=x$ $x\wedge x=x$; $x\vee…
Khanak
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Can someone explain how this question is reduced using basic postulates

I'm looking at some class examples on basic postulates and I can't figure out how the 2nd part is reduced (see below). Could someone explain it to me? eq: X='a'c+ac+'ac+a'c this is the part I do not understand, and could use some explanation using…
cdnicoll
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Need help with boolean algebra

This is a question from my school work. Although i have solved it, i can't seem to do it the way the question wants me to. The question involves you finding the complement of an expression and simplifying the results. The expression was…
Daraxxus
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Linearly separate a cube

I am facing the problem of the linear separability of a three dimensional cube. Let's take the opposite vertexes of the cube as $(0, 0, 0), (1, 1, 1)$. It is possible to split it with a plane in two tetrahedron-like parts, and so define two sets,…
Lorenzo Pistone
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Help on Boolean Expression Simplification

I got a question and I'm wondering is the way I solve it correct? $$xyz + x'z' + xyz' + x'y'z + x'yz'$$ $$= xyz + xyz' + x'y'z + x'yz' + x'yz' + x'y'z'$$ $$= xyz + xyz' + x'y'z + x'yz' + x'y'z'$$ $$= xy + x'y' + x'yz'$$
Donny Avaris
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Help at solving boolean function.

I`m having some difficulties solving a boolean expression (I am converting it to CNF form). The expression is: $$F = (Q_1 \to P1 \land \lnot P_2) \lor Q_1 \land P_2 \lor P_1$$ So i do not know, how to put the brackets properly. I know the…
Trom
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Transforming logic circuit to use only NAND gates

How would you go about transforming $BC'(A ⊕ D) + AD'(B' + C)$ to only use NAND gates? Please help. Thank you.
Ebu Potokombe
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Boolean law simplification

How would someone go about simplifying the expression: $((p \vee r)\wedge((p \wedge q) \vee (p \wedge ¬q)))\vee (p \wedge r) \vee \neg(p \vee q) \vee r$ Any help would be appreciated. EDITED: Is this a correct truth table?
Ebu Potokombe
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