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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 .

3083 questions
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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!
Ofir Attia
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Boolean Expression Problem

$$AB'C'D+ABCD$$ $$=AD(B'C'+BC)$$ $$=AD$$ I have simplified this expression right but for some reason I still get the answer wrong. The expression $AD$ does not match the original truth table. Please help.
Tuscan
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Please Help with this Boolean Expression Simplification

I have been asked to simplify the following expression in an assignment problem: X’YZ + XYZ + XY’Z’+XYZ’ + XY’Z’ + X’Y’Z’ + WX’Y’Z’ + W’X’Y’Z’ The result of the simplification should only be 2 terms. I have attempted many times and I have been only…
Clueless Coder
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Degree of boolean functions

How can we compute the degree of boolean function? I encountered with this,while solving a problem given in my assignment module which is, How many different boolean functions of degree 1 and 2 are there? The suggest answer in my module is $4$…
Quixotic
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Boolean Algebra Simplification - Weird Step

When reading the book Boolean Differential Equations(B. Steinbach, C. Posthoff), I stumbled upon the following demonstration of the orthogonality between the simple minimum and the simple derivative: $$ \underset{x_i}{\min}f(x) \wedge \frac{\partial…
Iorpim
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How can we show through Boolean algebra that if $ab = ac$, then $a\bar{b} = a\bar{c}$?

So I have this set theory expression that I'd like to show in boolean algebra. So if $A \cap B = A \cap C$, then I can show that $A \cap B^c = A \cap C^c$, since this is just $A \setminus B = A \setminus (A \cap B) = A \setminus (A \cap C) = A \cap…
user49404
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Are $(A \land \lnot B)$ and $(\lnot A \land B)$ universal gates?

Are $(A \land \lnot B)$ and $(\lnot A \land B)$ universal gates? (That is if we look at (A AND NOT B) as one individual gate, and (NOT A AND B) as another individual gate). Obviously these consists of two gates each, but im wondering if these are…
user366820
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Is this boolean answer correct?

F(x,y,z) = (x + y')(x + y)(xz') = (xx) + (xy) + (xy')+(y'y)(xz') = [x + (xy) + (xy') + 0 ] (xz') = [x + x(y + y') + 0] (xz') = [x + x(1) + 0] (xz') = [x + x + 0] (xz') = [x + x] (xz') …
Tsering
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Is integer division (from 0 to 3) a universal operator?

Given a function F that accepts two pairs of 2 bit integers (from 0 to 3), that returns the integer division of the two integers as a two bit integer. Is said function a universal operator? (Assume division by 0 is not possible). (1,0) / (1,0) =…
Alex Osheter
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does $B'C + BC' = 1$

I'm studying Boolean algebra: I know this is a straightforward answer. I'm a bit confused about if $B'C + BC'$ would be opposites in this case and would follow the rule that $A + A' = 1$ Or how can that simplify? Thanks so much!
Katie Melosto
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Boolean algebra how does $A'(B' *C+ B* C')$ simplify?

Does $A'(B' *C+ B* C')$ simplify to $A'(1)$? I'm a bit confused because I know that $A+A' *B = A +B$ so I'm wondering what happens in the above situation. I know this might be related to the two variable rule. Note $*$ represents AND and $+$…
Katie Melosto
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How to prove $(\overline{A} \cap \overline{B}) \cup (A \cap B) = (A \cup \overline{B}) \cap (\overline{A} \cup B)$

$$(\overline{A} \cap \overline{B}) \cup (A \cap B) = (A \cup \overline{B}) \cap (\overline{A} \cup B)$$ Note that $\overline{B}$ denotes the complement of B. One thing I notice is that $(\overline{A} \cap \overline{B}) = \overline{A \cup B}$ using…
jskattt797
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If you have a boolean function with only "true" and "don't care" (no false) outcomes, how would you write the equation?

In my homework I came across a situation where I had a Karnaugh map that only contained don't cares and trues. Since there are no false outputs possible, it seems like the equation would just be f(x,y,z) = TRUE. Am I right or am I missing…
Marty
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Prove that $A^c = (A^c∩B)∪(A^c∩B^c)$

Could someone help me with this problem? I have no idea how to attempt to solve it nor do I know where I can ask for help besides her.
Tom el Safadi
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Steps to Simplify Boolean Expression

Could someone please example how $(\bar A . \bar B . \bar C) + (\bar A . \bar B . C) + (A . B . \bar C) + (A . B . C)$ can be simplified to $(\bar A . \bar B) + (A . B)$ ? Here's what I've tried, but I don't trust all the steps: $(\bar A . \bar B .…
Robin Andrews
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