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 .

3083 questions
0
votes
1 answer

Is the power set of $\mathbb Z$ an algebra?

I have the following definition of an algebra: An algebra of sets is a family $A$ of subsets of a certain set $X$, satisfying the following rules: $\emptyset, X \in A$ If $a, b \in A$, then $a \cup b \in A$ If $a, b \in A$, then $a\cap b \in A$ If…
isawahatonce
  • 48
0
votes
1 answer

Karnaugh Map and Seven Segment Display Question

I am honestly confused over here. I understand how bit manipulation works. But when it comes to Boolean Algebra I seem to be a bit stumped. So if A = 1, then ~A = 0. But in this example (~A * ~B) + (~C * ~D) = 0 + 0 or 0 | 0 = 0. But in this example…
Kendrick Lamar
  • 103
0
votes
1 answer

boolean algebra, why is this try to simplify wrong?

so I have been trying to learn simplifying boolean Algebra, lets look at this term : $$ (a*b)+(a*\neg b)+(\neg a * \neg b)$$ I have several questions, I know how the right solution looks like but why couldn't I collect $a$ and $\neg a$? so : 1.…
Zesa Rex
  • 113
0
votes
2 answers

boolean algebra, simplify going wrong!

so this might sound stupid but I have a problem when it comes to simplifying terms. lets take this simple term as example (it was taken from a truth-table where these are the 0 results, that means DNF right?): $$\neg a * b * \neg c * \neg d + \neg a…
Zesa Rex
  • 113
0
votes
1 answer

Additive probability measures

Suppose that $B$ is an algebra of sets and $p$ is a finitely additive probability measure on $B$. Show that there cannot exist uncountably many disjoint sets in the family $[A \in B: \mu (A)>0]$. I am struggling to show this result. Thanks
juper
  • 267
  • 1
  • 10
0
votes
2 answers

Boolean reduction of $AB+(B+C)BC$

Reduce this Boolean expression $$AB+(B+C)BC$$ Please express step by step process to understand clearly.
Dhani
  • 31
  • 1
0
votes
3 answers

How does this Boolean simplification work?

The following expression: $$ABC + BCD + A'D$$ simplifies to: $$ABC + A'D$$ I just cannot understand how this comes about.
chomprrr
  • 103
0
votes
1 answer

How to find the sum of XOR's in this scenario?

I have two sets of whole numbers $\{s_1,s_2,s_3, \dotsc,s_n \}$ and $\{p_1,p_2,p_3, \dotsc, p_m\}$. Now I will take a number from first set, and XOR it with some number from set 2, and I want to find the sum of all the possible combinations. For…
aroma
  • 482
  • 4
  • 12
0
votes
3 answers

Simplify the boolean equation

I am trying to simplify this boolean expression: F = A B ((A + C')') + B (A C + A' B) + (A + B)(A' + C D) The resultant solution is supposed to be: F = A C D + ('A B) + B C But all I can get is F = A C D + ('A B) + A B C + B C D Help would be…
ro ko
  • 179
0
votes
1 answer

Error converting truth table into boolean exp

Again with a question about truth tables! Here there's an error somewhere... can you help me? This is my truth table: CD | 00 | 01 | 11 | 10 AB | | | | ------+----+----+----+---- 00 | 1 | 1 | 0 | 0 …
Cholesky
  • 15
0
votes
1 answer

Boolean algebra: if x ⊔ y' = 1 then x ⊔ y = x

I am new to boolean algebra questions so if anyone can help me pointing out thinking errors (if there are any) that would be fantastic. I am trying to solve the following: if x ⊔ y' = 1 then x ⊔ y = x Definitions: The problem with operators ⊔ and ⊓…
EconAleks
  • 1
0
votes
1 answer

simplify boolean expression

I have a boolean function. Unfortunately I am not able to simplify it to the minimal term. What I have done so far: $f = x_4 x_2 + \overline{(x_3 + x_2) \cdot 1 x_1} + x_2x_0$ $f =x_4 x_2 + \overline {(x_3 + x_2 )x_1} + x_2x_0$ $f = x_4x_2 +…
jublikon
  • 943
0
votes
2 answers

toggle boolean and more

Recently I used this to toggle a Boolean value, b being the current value and self.status being the result self.status = (b-1)*(b-1) This rather than use an if statement How could I use the same concept to toggle more than 2 values? (ie -1 0 1)
peterretief
  • 103
0
votes
1 answer

Changing from product of sums to sum of products

I have a function that compares two 2 bit numbers and this is the function for it in what I think is product of sums form but I need it in sum of products form. How do I convert it to the latter? EQU = (~A[1] | B[1]) & (A[1] | ~B[1]) & (A[0] |…
Dan Nguyen
  • 3
0
votes
1 answer

XOR gate with 4 inputs - truth table & MDNF?

I have difficulties with one equation. It's an XOR gate with 4 inputs. F(A,B,C,D)=(A⊕B)C+(B⊕C)(A⊕C) 'B' from the second bracket has a line above it , so does the 'A' from the third. I did the truth table,but once transferred to Karnaugh map, the…
Tisho
  • 1
1 2 3
…
64 65