# Tagged Questions

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### Simplify a boolean algebra expression: xy + xz' + x'yz

I need to simplify xy + xz' + x'yz into xz' + yz. I know that these expressions are equal in truth value, but I'm not sure how ...
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### Functions for boolean operators, that return 1 or 0

Are there any purely mathematical expressions that are equivalent to boolean operators and return $1$ or $0$? For example: $a > b$ Is there any $f(a, b)$ for which if $a>b$, $f(a,b)=1$ and if ...
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### The empirically-obvious statement about minimization of Boolean functions

The statement: $\forall f,g: \{0;1\}^n \to \{0;1\} \; (n > 0),$ if $$|f^{-1}(1)| > |g^{-1}(1)|$$ then $f$ has the (non-strictly-)simpler minimization than $g$. $\text{ }$ As mentioned, the ...
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### Finding a simple function for a given Karnaugh diagram

I came across one question in which the Karnaugh map for some function is given and using it, i have to find a simple function which gets mapped onto that map. My Attempt: Corresponding to every ...
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### Need help proving that $fRg \Leftrightarrow fg = f$ on $B^{n}$ to $B$ if and only if $f(b_1,…,b_n) \leq g(b_1,…,b_n)$

I'm trying to gather my thoughts for proving the following claim: For $fRg \Leftrightarrow fg = f$ on $B^{n}$ to $B$, show that $fRg$ if and only if for any input values $b_1,...,b_n$, we ...
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### Finding conjunctive normal form of a Boolean polynomial

I have to find the conjunctive normal form of the following Boolean Polynomial : $(x_1+x_2+x_3)(x_1x_2+x_1'x_3)'$ I simplified this polynomial to get $x_1x_2'+x_1x_2x_3'$ for which i then formed the ...
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### Simplification of a boolean polynomial

I have to simplify the following Boolean polynomial using $x\land y$ = $xy$ and $x\lor y$ = x+y : $xy'+x(yz)'+z$ =$xy'+x(y'+z')+z$ =$xy'+xy'+xz'+z$ =$xy'+xz'+z$ My book gives the following ...
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### Minimization of boolean function using Quine–McCluskey algorithm

I have a boolean row. It looked like this: Y = 0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0 Then I converted it to: f(x1,x2,x3,x4) = 0101 ∪ 1001 ∪ 1010 ∪ 1100 I divided it into groups: 0 | - ...
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### Boolean formula over 64 Boolean variables X

This question comes from this homework assignment from ECS20 at UC Davis. Chess is played on an 8 x 8 board. A knight placed on one square can move to any unoccupied square that is at a distance ...
I do not understand this at all. Find the sum-of-products expansions of these Boolean functions. $F(x, y, z) = x + y + z$ $F(x, y, z) = (x + z)y$ $F(x, y, z) = x$ $F(x, y, z) = x y$ ...