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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Prove System is Boolean Algebra

There is a mathematical system with 2 operators # and & and 4 different inputs/variables. The 2 operators are defined in the picture. Chart I need to prove that the system is boolean algebra and to find the complements of 0,a,b,and c. Now, to prove…
user3728320
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Simplify Boolean Expression Given Truth Table

Truth Table I have the truth table above which gives the minterm expression $$F = (\neg a \land \neg b \land c) \lor (\neg a \land b \land \neg c) \lor (a \land \neg b \land \neg c) \lor (a \land b \land c)$$ but I'm unsure how to simplify it using…
smd
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Help with Boolean Expression Simplification

I know that $$(\neg a \land \neg b \land \neg c) \lor (a \land \neg b \land c) \lor (\neg a \land b \land \neg c) \lor (a \land b \land c )$$ and $$(\neg a \land \neg b \land \neg c) \lor (a \land c) \lor (\neg a \land b \land \neg c)$$ are…
smd
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On a theorem concerning free Boolean algebras

In Sikorski's book "Boolean Algebras" (3rd edition), p. 42, one finds the following theorem: In order that $\mathfrak{A}$ be a free Boolean algebra with $n$ free generators, it is necessary and sufficient that $\mathfrak{A}$ be the Boolean product…
user60264
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Adjust the result of a boolean expression

I need to solve this in boolean algebra: $$B(A+(B'+ A)')$$ Here is my attempt: $$B(A+(B'+ A)')=B(A+(BA'))=B((AA')+(AB))=B(0+AB)=B(AB),$$ and the result should be just $B$. Should I just decide what is the right result (because I see it depents on…
trolkura
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how to draw a truth table for following logical expression?

It's a question in my assignment, which I don't really understand it. However, there is an example here. e.g. A computer uses the following logical expression to control a finger print scanner. F(A, B, C, D) = Σ (0, 1, 4, 5, 12, 14) What will be…
Bsonjin
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Basic prove that boolean function is self-dual

I'm tring to prove this function: $$ f(x,y,z) = x'y'z'+x'yz+xyz'+xy'z $$ is self-dual, I've tried some basic manipulations like using double not on the function with de-morgan rules but got no results. I also looked at Kerno's map and it's…
Tal Yitzhak
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Have I simplified this Min-term Correctly?

I have got two different solutions and I would like to know if they are correct, I would be very grateful if you could let me know if they are correct or what I can do to correct them. Solution 1 A'BC'D' + AB'C'D' + AB'CD' + ABC'D +ABCD' A'BC'D'…
unreal1357
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don't understand something in boolean algebra solution

I asked a question earlier and got the solution https://gyazo.com/372f0352b7d8aeb180586ac5218dd1bc I understand it all apart from this part AB(C⊕D)+D′(AB′+A′B) How can you use D′(AB′+A′B) if D is already used in AB(C⊕D) I might just be being…
unreal1357
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Which form of the function is simpler?

I'm simplifying function in Boolean algebra. Which form is simpler: $AB' + C'D + A'BC$ OR $DA' + C'D + AB'$ Second form has less letters but overlays itself at more spots. Which one is simpler?
rob
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Simplify the boolean expression

Kindly help in Simplifying Y = BCD + BC'D. I have been trying to simplify the expression for sometime now, using the the 10 rules but cannot simplify fully.
mandan
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Simplify boolean algebra : (w'x+yz')((xz+w)(y+xz'))'

(w'x+yz')((xz+w)(y+xz'))' I gotten the answer w'xy'z+wyz' however the answer sheet was w'xz' +w'xy'z+w'yz' can anyone confirm?
kero
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Extracting information from simultaneous boolean AND, XOR, and NOT

I'm looking to extract some information from a series of equations with AND, XOR and NOT. I've already covered all of the easy parts using various boolean identities, so I'm looking to now determine if there are any non-obvious sources of…
DeadMG
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Use Boolean algebra properties to prove the given equality.

Use Boolean algebra properties to prove the given equality.. How do I do this? $\bar{x}yz + \bar{y} + \bar{z} = \bar{x} + \bar{y} + \bar{z}$ I know $x + \bar{x}y = x + y$ I also know: $\bar{x}yz + \bar{y} + \bar{z} \equiv \bar{x}yz + \bar{yz}$ so I…
Shammy
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Simplify boolean expression $AB + A\bar B+ ABC $

Simplify $AB + A\bar B+ ABC $ I've been trying to simplify for a good while now. I'm using only the 10 rules but cannot find a way to simplify fully.
GNov
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