Boolean algebras are structures which behave similar to a power set with complement, intersection and union. Questions regarding Boolean algebras as structures, or regarding functions defined from/to Boolean algebras fit into this tag very nicely.
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Simplify Expression Question
Anyone can tell me if I can simplify this expression more?
I Simplified this function => $minterm(1,3,4,6,7,9,10,11,12,15)$ to this expression:
$W'X'Z+W'Z'X+WYZ+W'XYZ+WX'Y'Z+WX'YZ'+WXY'Z'$
Thanks!
0
votes
0answers
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Write the following functions in algebraic sum of multiples or multiplying Amounts. If possible,simplify the expression
Write the following functions in algebraic sum of multiples or multiplying Amounts. If possible,simplify the expression
The Question is:
$F(A,B,C): Maxterms(4,5,6,7)$ :
$M4 = 100 => A'+B+C $
...
0
votes
1answer
15 views
Single variable true or false statements
If I have a true or false statement S, depending on a varible x, is there some standard function or opperation in formal logic, that takes the statement S and the variable x, and outputs $1$ if ...
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0answers
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What is the order of steps when simplifying functions with NOT
What is the order of steps when simplifying functions with NOT
I need advice on simplifying the following function, I have a function with several stages of NOT, Do I followed the steps?
Thanks!
0
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1answer
15 views
Expressions Simplifications Boolean Algebra
Expressions Simplifications Boolean Algebra
I started simplifying function and got to the detailed picture and wanted to know if I can reduce the above expressions, for example :
Y'.X'.Y = 0 ?
...
0
votes
2answers
26 views
Boolean Algebra Simplification Question - Proof of equation
Boolean Algebra Simplification Question - Proof of equation
I`m trying to proof this equation:
X'.Y' + Y'.Z + X.Z + X.Y + Y.Z' = X'.Y'+X.Z+Y.Z'
What your are suggesting? to add some
...
2
votes
0answers
31 views
Basis of a Boolean Algebra
I have a construct that I proved forms a (finite) Boolean Algebra of sets over a given universe.
My questions are as follows:
Do I immediately know that there exists a unique basis for it?
If yes, ...
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2answers
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Simplifying boolean expression: $!(x!z+y!z+xy+z)$
This is the expression:
', ! not+ or
$((x'y'+z)'+z+xy+wz)'$
After some steps I can get
$!(x!z+y!z+xy+z)$
How can I continue from here?
-2
votes
0answers
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Monotone and linear boolean functions ,intersection [closed]
Find the power of the intersection of monotone and linear boolean functions of n variables ,that is $|M\cap L|$
8
votes
1answer
128 views
Stone's Representation Theorem and The Compactness Theorem
If you're working on $ZF$ and you assume the compactness theorem for propositional logic, then you have the prime ideal theorem, and thus you can show that the dual of the category of Boolean algebras ...
1
vote
1answer
46 views
Free algebra (Boolean algebra)
Could someone give me a simple explanation of Free Algebra on $\kappa$. How to construct free($\omega$).
here is it says
http://en.wikipedia.org/wiki/Free_Boolean_algebra
free($\omega$) is equal to ...
2
votes
2answers
68 views
How to prove that $(A \lor B) \land (\lnot A \lor B) = B$
I know this is fairly basic, and I understand that it becomes
$$
\begin{align}
(A \land \lnot A) \lor B \\
F \lor B \\
B
\end{align}
$$
However, I can't work out how to prove that it becomes that ...
2
votes
1answer
58 views
Can boolean homomorphisms of boolean algebras correspond to ultrafilters?
I am trying to solve 5th problem in Exercises 2.9 in Awodey's book on page 55:
Show that for any boolean algebra $B$, boolean homomorphisms $h :
B \to 2$ correspond exactly to ultrafilters in $B$.
I ...
3
votes
1answer
39 views
How do I find the size of this set?
For homework, I need to show that the size of a certain set is $\le 2^{(3n)^k}$ but I'm not getting this (I think I may just misunderstand how the set is defined).
So the set is defined as follows:
...
2
votes
1answer
29 views
Boolean Algebra Question
my problem is ,Please give the algorithm: how can rewrite an arbitrary propositional formula alfa(α) into a proposional formula beta(β) so that beta does not contain disjunction(∧) and alfa ...
