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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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Finding number of Boolean algebras

How many Boolean algebras are there with four elements $0,1,a,b$ ? I don't know how to proceed with this. Any ideas ?
johny
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BOOL algebra : simplifications

I have this expression : (A && B) || (A && C) || (B && C) I don't understand which steps I need to to to get this expression : (A && B) || (C && (A XOR B))
jlink
  • 367
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How to simplify following boolean expression? A+A'BC+BC'?

please help I'm stuck. I'm trying to solve this. so far I have: a) a+b+c b) a+bc c) a+b d) a+b but for e) I can't progress further since I don't know how to deal with a'bc in this case. anyone so kind to please help me?
Shads
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How to simplify in boolean algebra

I have some homework I can't seem to figure out. The assignment causing problems is devided into two parts; The first is to determine the inverse formula for a given formula (so the S = F'). The second part asks me to simplify the answer to the…
Lg102
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Terminology: algebras, sigma-algebras, complete algebras...

There are 2 things which create a lot of confusion in my mind. 1) I know that every sigma-algebra is an algebra. But not every algebra is a sigma-algebra. Put differently, it seems that sigma-algebras are subsets of algebras (?). On the other hand,…
student
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Boolean Simplification for Kmap

Diclaimer: This is not a homework assignment, it's a practice sheet that already has answers provided and is not graded in any way, however the steps are not shown hence the question. I'm having issues converting the following expression into one…
Patryk
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Boolean algebra simplification.

I start with: $$\bar{A}\bar{B}\bar{C}+\bar{A}BC+A\bar{B}\bar{C}+A\bar{B}{C}=A\bar{B}+\bar{B}\bar{C}+\bar{A}BC$$ then I…
Vector_13
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Boolean Functions with p,q,r

Please give me feedback for my answer to this question. Question: (1) Are the boolean functions $(p \land \neg q) \lor ( \neg r \land q)$ and $(p \lor \neg q) \land (r \lor \neg q)$ equal?. Explain your answer. My Answer: - No, they are not equal…
user142943
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showing Boolean algebra equality

I have this exercise in my worksheet : Show that x (z ⊕ y) = xz ⊕ xy I reached this in solving it , but didn't reach the final equation x(z'y + zy') xz'y + xzy' please can someone show how
MathDisease
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Boolean function construction

I need some proof on this statement that not every boolean function is equal to a function constructed by only using ∨ and ∧. I need a boolean function that does not constructed using ∧ and ∨ which I am assuming that it is p⊕q but I need help on…
user130602
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Boolean algebra simplification question

I'm trying to simplify the follow SOP expression: $\bar{A}$$\bar{B}$$\bar{C}$ + $\bar{A}$B$\bar{C}$ + $\bar{A}$BC + AB$\bar{C}$ Using a K-map (unless I've erred) it should simplify to: $\bar{A}$$\bar{C}$ + B$\bar{C}$ + $\bar{A}$B However, I can't…
CSpadawan
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Boolean Algebra, Simplification: Sum of products from truth table

Based on a previous question (and this ought to be the last of this sequence I promise), I just need to know one more thing. According to this truth table: I'm told the answer I should be getting by using the sum of products method on the truth…
Hamster
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prove that there does not exists a boolean algebra containing only three element

please prove that there does not exists a Boolean algebra containing only three elements .prove it with example so that i can understand easily.i cant understand the question and i could not tried to prove it
user137249
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Boolean functions built from $\wedge$ and $\vee$

Prove that not every Boolean function is equal to a Boolean function constructed by only $\wedge$ and $\vee$. Please can you help me giving some hint.
user136423
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Discrete Mathematics (boolean)

Either exhibit 333 different boolean functions on the three variables p; q; r, or prove that there aren’t 333 different such functions $p$ $q$ $r$ $0 0 0$ $001$ $010$ $011$ $100$ $101$ $110$ $111$ $f(0,0,0)$ : $2^8=…
Kit lai
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