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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 .

3083 questions
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Finding the contrapositive of the statement "I go to school if it does not rain"

I got this question in a exam.There were two more statements in the examination(but they were quite clearly wrong).However I got stuck between these two statements.The contrapositive of the the statement "I go to school if it does not rain"…
User98274
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Boolean Expression Simplification (De Morgan's)

I need to prove that: $$ !(!(X.W) + !(X.Z))) = X.W.Z $$ I have tried multiple approaches but cannot figure this out. Using DeMorgan's theorem, I break the negative sign binding $XW$, and $XZ$, and change their sign: $$ !((!X + !W + !X + !Z)) $$ By…
zyked
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How can I rewrite this xor formula to generate cnf formulas

$$ \bigwedge_{c=1}^n\bigwedge_{i\epsilon S}\bigoplus_{r=1}^nX_{irc} $$ I have tried $$ \bigwedge_{c=1}^n\bigwedge_{i\epsilon S}\bigwedge_{r_1=1,r_2=1}^n(X_{ir_1c}\vee X_{ir_2c})\wedge(\neg X_{ir_1c}\vee \neg X_{ir_2c}) $$ But this does not work …
sherif
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Boolean Function with ^ and or

Please provide feedback on my answer to this question. Question: Prove that not every boolean function is equal to a boolean function constructed by only using ^ and or. Answer: True, Suppose that a function f(m,n)=m exclusive n using only ^ and…
user142943
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Proving Boolean Functions

Please check my answer to this question and give me feedback . Question: Either exhibit 333 different boolean functions on the three variables p,q,r, or prove that there aren't 333 different such functions. My Answer: -For three variables p,q,r it…
user142943
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how to make a truth table from an boolean expression

I am trying to make a truth table from an SOP boolean algebra expression. I understand AND, OR, NOT truth tables. I just don't understand these types of tables and their outputs. This is the expression: $$A'BD' + BCD + ABC' + AB'D = A'BD' + BCD +…
Corey J Mattis
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Assignment for discrete mathematics

How can I prove that not every boolean function is equal to a boolean function constructed by only using ∧ and ∨?.Need help in proving it.
Niraz
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What are three possible ways to express the following Boolean function with eight or fewer literals?

F= A'BC'D + AB'CD + A'B'C' + ACD' I assumed that the question was asking for me to simplify. I placed the terms into a kmap and have gotten SOP F= A'B'C' + A'C'D + AB'C + ACD' or POS F= (A+C')(A'+C)(B'+C'+D')(A+B'+D). Neither of which are eight or…
Landry
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Boolean Algebra, Simplification: Sum of products

Possible Duplicate: Boolean Algebra, Simplification: Don't know the method used Based on a previous question, the answer I got for the "sum of products" method was: RC' + RCG' + RCGM' Just for completeness, can someone help walk me through to…
Hamster
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Logic subject-reductio ad absurdum

Can you solve this using method reductio ad absurdum? $\text{1})\ A ↔ (\neg B v C)$ $\neg A$ $\text{______________}$ $\neg B$ $\text{2})\ \neg(R∧ (S v T))$ $\text{3})\ R∧\neg T$ $S$ $\text{______________}$ $\neg R∧ S$
Jele996
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Boolean algebra question: Converting between sum-of-products and product-of-sums

NOTE: $b'$ means $b$ not I'm trying to convert $ab'd + ab'cf$ to product of sums form My professor gave us the following hint: "Invert the equation, reduce it to sum-of-products, then invert it again. The result will be the original equation, but…
user13327
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Expression conversion using de Morgan's laws

I'm sorry strongly, because it's a very dummy question... I have an example in the algebra of logic. I need to convert an expression using the rules of de Morgan - replace by the conjunction of disjunctions, and disjunction - on the conjunction. I…
dark
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Karnaugh Map for an expression with two terms

When I have an expression such as: $f(x_1,x_2,x_3)= \sum m(1,4,7)+ D(2,5)$ What do I do with the part D(2,5)? Do I make a second k-map just for that term and OR(+) it to the expression or should I just put the terms (2,5) in the original k-map and…
Nick
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Can this be simplified any further? (Boolean algebra)

I've been working on this expression, but all my attempts have failed to simplify it further. $$A'.B' + A'.B.C' + A'.B.C + A.B'.C'$$ I have tried to pick out $A'$ based on the distribution law: $$A' (B' + B.C' + B.C) + A.B'.C'$$ Then I tried to…
dntk
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Converting to complements

Let's say I wanted to convert the ands and positive variables to their complements and ors. Would this be correct? $$DE=$$ $$(DE)''=$$ $$(D'+E')'$$ Or another example: $$D'E=$$ $$(D'E)''$$ Can you break the last one down further?
munchschair
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