# Tagged Questions

Questions on the functionality of Mathematica for Boolean computation.

6k views

### Intersecting graphics

Does the Mathematica graphics system have any concept of intersecting graphics? I've not found much in the documents so far. For example, if I want to show the intersection of two shapes: ...
2k views

### Are there “All” and “Any” functions in Mathematica?

In Python, there is a function all which returns true if all of its arguments are true, and any which returns true if at least ...
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### Applying And to lists of Booleans

I'd like to take {True,True,False} and {True,False,False} and apply And to get ...
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### Why is SatisfiabilityCount faster than SatisfiableQ?

Consider the following (large) Boolean expression, which arose in a SAT problem. (The expression is not satisfiable.) ...
624 views

### Binary decision diagrams (BDD)

I would like to use Mathematica to help me simplify a given Binary Decision Diagram (i.e. pick the optimal variable ordering). I don't seem to find anything at all on the topic, although it is ...
883 views

### How to solve the liar problem?

In an island live two kinds of people: liar and truth-teller, the former only tells lies and the latter only tells truth, now there're two men A and B from the island, A said: "B is a truth-teller." B ...
1k views

### Simplify assumes Boolean 1 and 0 in logical expressions

Per this chat discussion and this previous question where I encountered the strange behaviour: ...
1k views

### Implementation of a new Game of Life Rule

I need to implement a new "game of life" in Mathematica: I have three states — black, red and white. Black means go forward, red go back and white take no action. I would like to implement the ...
496 views

### Bitwise operators - Hamlet for Mathematica

What is the best way to check this famous equation: 0x2b || ~0x2b == 0xff Mathematica doesn't seem to have a handy bitwise negation operator. The best thing I ...
598 views

### Prenex and Skolem normal forms

In MMA version 7 there was a big advance in logic support ("Boolean computations" is the official name). This was not further developed in version 8.0. So now we have a fairly robust support for ...
287 views

### How to simplify Boolean expression

I would like to simplify $$((p\oplus q)=True)\wedge(p=True)$$ to $$q=False$$ I was hoping BooleanMinimize[((p ⊻ q) == 1) ∧ (p == True)] would do the trick, but ...
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### “And” to continue evaluation after “False”

Below, is it possible to print No and have x be 2. That is, I'm looking for an And-like function that looks at all arguments ...
186 views

### How to get the boolean value of an inequality involving an InterpolatingFunction?

Here's the code: yan = FunctionInterpolation[x^2, {x, -1, 1}]; FullSimplify[yan[x] > -1, -1 < x < 1] Needless to say, what I expect to see in the output ...
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Suppose I have a list of the form: list = {a, b, {c, d}, f, {g, h}} i.e. an element of the list could be another list. I want to 'thread' each element of the ...
201 views

### Short circuit logical operators [duplicate]

Suppose I want to compute $f(1)\vee f(2) \vee \ldots \vee f(10^{10})$, but I know a priori that $f(n)$ is True for some $n \ll 10^{10}$ with high probability. For ...
421 views

### Using Boole to integrate over region

I have a complex and long piecewise function to integrate, so I have written a Mathematica script that cuts the whole range of integration, evaluates the integrand in each region and then integrates ...
132 views

### Theorem Proving

It's a hard for me to write english so I'll try to go straight to my problem. There is abstract predicate f, that takes two parameters. There are also two other ...
184 views

### Can I define an axiomatic (Boolean algebra) system and prove theorems using Mathematica?

The general question is Can I define an axiomatic system and prove theorems using Mathematica? The more concrete one is about Boolean algebra. I consider this axiomatic Boolean algebra system (...
393 views

### Fast method for combining two lists

I have two lists, v1 and v2. Each element of the lists may be positive or negative. I want to create a list ...
262 views

### Importing an array from text file and convert it to truth table

I am new to Mathematica, and would like some help in the following operation. I have a truth table stored in a text file. I want to read this in Mathematica, and find its Boolean Rule. Suppose I have ...
146 views

### Is there an equivalent of Sum for And?

Is there an equivalent to Sum for And? That is, just like instead of ...
276 views

### Convert boolean test function to pattern?

What is a "reverse" to MatchQ? MatchQ converts pattern into boolean function. So how to convert back? Suppose I want to use ...
257 views

### Region Intersection for MeshRegion objects embedded in 3D

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will ...
180 views

### Sequence and boolean And

I'm trying to figure out if a calculation result it's a valid result. As it return a matrix, I need to test that every element it's a number, so I thought this could work... ...
285 views

### How to rewrite this function to be faster: Find sub-matrixes of boolean board which imply a given boolean pattern

I have Boolean matrix A (called "board") and Boolean matrix B with smaller dimensions (called "pattern"). I am trying to find sub-matrixes C of A such that C has same dimensions as B, and TableImplies[...
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### How to evaluate Boolean expression and get an answer in bitwise form?

I am trying to evaluate the following expression: 11000 AND ( 01011 OR 11011 ) I am able to get the answer on paper. The answer is: ...
850 views

### Converting truth tables to boolean expressions

I have a truth table for a Boolean expression represented like this ...
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### Using TrueQ with conditions

Say I want to ask Mathematica whether $|x| = x$ for all $x > 0$. Obviously, if I try TrueQ[Abs[x] == x], I get False, ...
296 views

### Simplify binary expressions

Is it possible for Mathematica to do simplifications for expressions where the variables are binary, such as: a + b = 1 + 2*c => a + b = 1 Here c must be 0 because if it is 1, the RHS is 3 but ...
142 views

### Defining an Implies operation that works for Boolean matrices

I have two Boolean matrices, that both have dimensions m x n. I want to create a function TableImplies, which would return True ...
105 views

### Defining an arbitrary binary relation

I am trying to define some binary operators. A binary operator operates on a set of variables V and is defined by a subset S of pairs of those variables {Vi,Vj}. For example, "=",">",">=" are all ...
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### How to negate a boolean vector?

The !True returns False but how can I negate a boolean vector such as {True, False, True}? ...
100 views

### Applying boolean logic to a 2D array

How can I make a function that creates a particular size 2D matrix that determines "True" or "False" if a random value between 0 and 1 is at or below a certain number? Below is what I have written but ...
88 views

### Ask Mathematica if there exists a value that satisfies conditions

I would like to build a function that returns true if there exists even one value of xg1 such that having as inputs Mtot, PL, xg2, mac, xga, and defining ...
533 views

### Matlab-style Find in Mathematica? Value list and Boolean List, how to select values according to the boolean list?

I want to select elements with the true value (Indices list) in the corresponding point to the value list (MCS). Is there anything like Matlab-style Find to get the indices of true values in the ...
112 views

### Boolean algebra does not simplify

I am doing some simple Boolean algebra and wanted to perform some calculations in Mathematica but found it doesn't work. Let us consider the expression: ...
414 views

### Given a system of inequalities, how to make Solve find out that two variables should be equal?

Given two boolean variables x1 and x2 (in the sense that they are in the range [0,1]), if I try to solve the following equation system with Solve: ...
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### Boolean function from incomplete truth table

BooleanFunction in mathematica can convert an input truth table to a Boolean function. It can do so even if the truth table is incomplete. But the interpretation of truth table obtained from such an ...
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### Converting Boolean functions to polynomials

We can generate a Boolean function of $n$ variables (take $n=4$ as an example) as follows: f = BooleanFunction[10, 4] I want to express $f$ as a polynomial. This ...
173 views

### What are the steps using boolean algebra for transforming one equation into another?

I have a special case where I have two equations, which I have solved in a better and quicker way, but I need to solve with Boolean algebra. Using the laws of Boolean algebra, I have to prove that ...
611 views

### Creating a Specific Boolean Function

How can I implement a Boolean function F(A,B) that has outputs that are not specific and, therefore, the truth table output of this two-input function will be (a, b, c, d) -- here the first term ...
96 views

### How to combine all possible N boolean values?

Is there any simpler formula than Tuples[{False, True}, 3] to generate tuples of all combinations of boolean values?
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### Infinite sums with Boole and EvenQ

Suppose I am interested in a sum across a set of even numbers, such as: Sum[x, {x, 2, 20, 2}] 110 or ...
750 views

### 3D Contour Plot parts of sphere with gradient less than 0, equal to 0 and more than 0

I want to plot only parts of the sphere of radius 1 where the gradient $\frac{\partial z}{\partial x}$ is < 0, = 0 and > 0. The full sphere is given by: ...
153 views

### Conditionals slower than operators?

I want to make my application faster. I tried to replace an If condition with operators. The If condition is ...
88 views

### How can I draw truth tables using Mathematica [duplicate]

For instance, the given expression p ⊕ (p v q) In the problem I'm trying to solve. There's a Mathematica answer to this: ...
79 views

### Discrete Measure between Binary Vectors

I would like a discrete distance measure between two binary vectors (or strings). Like HammingDistance but I want the vectors to be considered closer if they have ...
186 views

### 3D Contour Plot - parts with gradients less and more than zero

I'm trying to plot sections of the 3D Contours, with gradient less than zero, and more than zero and equal to zero. It manages to solve for the derivative, but when I apply the conditions ...
How to generate the truth table to show that $p \implies (q \vee r)$ is equivalent to $(p \wedge \neg q ) \implies r$ ? Can I use BooleanTable?