Mathematics Stack Exchange
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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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Boolean Simplification $ABC' + BC'D' + BC + C'D$

I'd like to simplify this equation: $ABC' + BC'D' + BC + C'D$ prove it to $B + C'D$ My attempt is : $$\begin{align} &= ABC' + BC'D'(A+A') + BC + C'D\\ &= ABC' + ABC'D' + A'BC'D' + BC + C'D\\ &= ABC'(1 + D') + A'BC'D' + BC + C'D\\ &= ABC' + A'BC'D'…
Hermon Jay
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Boolean expression explanation

Could someone explain how to get the following Boolean expression in its simplest form, I am having difficulties working it out step by step $$A+B+A*B$$
Mark Sharman
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Delove the truth for the three function same table

Given Boolean functions: $F(x,y,z)=x'.(y'+z')(x+y'), G(x,y,z)=x'.(z+yz')(x\oplus zy')$ Develop the truth table for the three function in the same table
user323601
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Does this always evaluate to true?

This expression: $1 \lor (0 \land 1 \land 1 \land 1 \land 1 \lor 0)$ Regardless of how order of operations inside the parentheses are taken, which are ambiguous, the fact that it is and Or operation with a 1 on the outside will always evaluate to…
op_finales
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Simplifying a boolean expression without using sum-of-products

Yes this is for a school class, and no I'm not asking anyone to do my homework. This is from an example. I have a boolean algebra expression that I have to simplify. I also have the answer simplified expression. However I can't seem to get from the…
Brian H.
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Simplify expression in Boolean algebra

In Boolean algebra, I need to prove that $AB+AB'C+BC'=AC+BC'$ and $(ABC)'(A+B+C)=A'B'C'$ Are both the questions correct?
user3575652
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Resolution of a Boolean Function

I have to solve this simple boolean function : $$f_1 * f_2 = (x_1 + x_2) * (!x_1 + x_3)$$ The solution is : $x_1*x_3 + !x_1*x_2$ Can anyone make a step by step solution because after getting : $$x_1*x_3 + x_2*(!x_1) + x_2*x_3$$ I don't know how to…
Alfonso
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Is there a proof for the FOIL method in Boolean algebra?

The FOIL method is the special case of multiplying algebraic expressions using the distributive law and is shown here: What does the proof for this look like using Boolean algebra?
user280800
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Boolean Algebra - $ABC+B'=AC+B'$?

I'm doing a bit of homework, and it says to prove or disprove the statement $XZ+X'Y'+Y'Z'=XZ+Y'$ If you do a truth table and take the sum-of-products, you can eventually simplify the equation down to $XYZ+Y'$. Now that was way too close for me to…
Robert M
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Representing Boolean expressions in a truth table.

Right so I'm trying to understand truth tables in the context of digital logic. And paticularly with lettered boolean expresssions. Now I do understand truth tables, you have either true or false as the value, and you have some operators that…
user310998
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How does one simplify this boolean expression?

(a + b)(b' + c')(a + b' + c) where b' = b not and c' = c not. I tried distributive because I'm not very good at applying the properties when multiplication is applied but I can with addition. (a + b)(b' + c') = ab' + ac' + b'b + bc' = ab' + ac' +…
Sal
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Do we assume a value to be true be considered as 1 in algebraic manipulation?

In my Digital Logics class, we are doing boolean algebra. In the case where $ a * b * c $ (a and b and c) can we assume either of those values to be 1? so can we say that $a * b * c = 1 * b * c$, in which case that would be $(a + a') * b * c$?
hs2345
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how solve the boolean expression

so my question is prove the following relation and solve the boolean expression. i'm stuck. because usually i solve the question is not like this. i) AB+ABC+ABC=AB ii) Z(Y+Z)(X+Y+Z)=Z
exia
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Why does the M AND Q term disappear?

Trying to solve a Boolean algebra expression which simplifies midway down to $$(Q \lor (M \land \lnot N \land \lnot G)) \land (M \lor N \lor G)$$ It seems the final result of the distribution should be $$(Q \land M) \lor (Q \land N) \lor (Q \land…
aftrumpet
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Problem with transformation of Boolean expressions

Having some problem with beginner boolean algebra. Somehow I can't figure out these two problems. Show that LHS is equal to RHS: $wx + w'y + xyz = wx + w'y.$ Can't find a way to "remove" $xyz$. $zy' + yx' + z'x = z'y + y'x + zx'.$ Tried different…
Eqstor
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