# Tagged Questions

Questions on use and formulation of logical operations, including both functions for programming and for mathematical operations.

4answers
5k views

### Elegant solution to the Zebra [logic] Puzzle (“Einstein's Riddle”)

The famous Zebra Puzzle (Wikipedia), often called "Einstein's Riddle," is a logic puzzle that can be solved deductively by applying a list of logical rules. One version of the riddle (from Wikipedia) ...
1answer
642 views

### How can we create Randolph diagrams in Mathematica?

I have become fascinated with Randolph Diagrams and was wondering how we would create the diagrams from logical sequences using Mathematica? It looks like it would be a combination of logic and ...
2answers
891 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 ...
0answers
131 views

### Logical AND of multiple patterns

Mathematica provides an equivalent for "logical OR" when pattern matching, using Alternatives or the infix | operator. For ...
1answer
172 views

### Is there an easy way to do set counting in Mathematica?

I'm using counts of elements in sets, along with logic. So, for instance, I'd like to determine if Count[$a \land \neg b$] = Count [$a$] - Count[$a \land b$] ...where ...
2answers
265 views

### TrueQ returning False on true statement

Why does TrueQ return False on the following? TrueQ[Log[2]/Log[8] == 1/3] (* False *) ...
3answers
1k views

### How to prove an expression by method of mathematical induction?

I want to prove the expression $$1^2 + 2^2 + 3^2 + \cdots + n^2 = \dfrac{n(n+1)(2n+1)}{6}$$ by method of mathematical induction with Mathematica, but I do not know how to start. How do I tell ...
2answers
148 views

### FunctionInterpolation and Which combine badly

Update 2: Got two solid answers, but had trouble implementing one, and found the other could only save me computation time by sacrificing accuracy. So I chose neither as an official answer, but they'...
3answers
422 views

### What exactly is Implies? Is it a logical test?

I ran the following to simplify my logical test (expecting something in terms of And and Or ...) ...
2answers
175 views

### Equality and Quantifiers

I am new to Mathematica and to Math. I do not study math in English, so please bear with me as I try to state my questions.. This is what I am trying to "solve": $$∃!x : A(x) ⇔ ∃x : ¬A(x)$$ In ...
2answers
267 views

### How to “ReplaceAll” using a set of conditional expressions instead of a list of rules [closed]

Suppose that I have two linear functions f[x_] := f0 + f1 x g[x_] := g0 + g1 x and a (possibly rather complicated) set of conditional expressions, obtained ...
0answers
157 views

### Logic programming with Mathematica

My question is: Wikipedia says that there is logic programming paradigm support in Mathematica (like In Prolog). Could anyone provide me with an example of using this paradigm in Mathematica?
0answers
100 views

### Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite Reduce[{Norm@{c[1], c[2], c[3]} == 1, 0 <= c[1] < c[2] < c[3]}, {c[1], c[2], c[3]}] ...
1answer
54 views

### Clues on theorem proving tools?

I'm trying to prove $[a \cup (b \cap c ) = (a\cup b)\cap (a\cup c)]$ with mathematica. But I don't know what function I should use. I've rewritten the sentence in the following way: ...
1answer
177 views

### Mathematica as Answer Set Programming (ASP) engine?

Maybe I need to rephrase this question, so that it might receive some attention: Are there any packages or examples of how to put Mathematica to good use in the field of ASP (Answer Set Programming) ...
2answers
410 views

### How to determine all cases consistent with constraints

Suppose that $(i, j), (k, l)$ and $(m, n)$ are pairs of non-negative integers, satisfying the following constraints: $$i < j,\;\; k < l, \;\; m < n$$ and $$(i, j) < (k, l) < (m, n)$$...
4answers
300 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 ...
2answers
69 views

### Creating Boolean expressions over a set of indexed variables

I've read lots of examples here on how to set one matrix Equal to another, but how do you nest And and ...
2answers
56 views

### Boolean value of proposition assuming previous boolean values of parts of the proposition

Is it possible to ask Mathematica to give us the boolean value of a proposition assuming the boolean value of some parts of it? For instance, give the boolean value of $p\vee q$ assuming that $p$ is ...
1answer
55 views

### How to get Mathematica to make further simplifications to conditional expressions than it has already made?

I have the following Mathematica result under the assumption that {ax, bx, px, ay, by, py} \[Element] Reals, and after refinement by ...
1answer
106 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 ...
1answer
43 views

### Getting a set of disjoint regions from the set of overlapping regions

Suppose I have two overlapping regions $R1$ and $R2$ looking like this: ...
0answers
65 views

### Simplifying between set theory and logical connectives

I'm trying to find out how to switch between set notation and logic, but am having difficulty. For instance, I know that the following two expressions are equivalent ...
0answers
316 views

### Reference request for logic programming in Mathematica

I'm learning Mathematica(v8) to use it to program formal logic. Can anyone recommend a logic-specific tutorial text? A reference list of logic-related functions would also be very appreciated!
1answer
95 views

### How to do symbolic logic in Mathematica

I'm currently in Symbolic Logic with homework assignments (not asking for people to do my homework for me) with questions such as the following: (derive the conclusion using the eighteen rules of ...
1answer
95 views

### Make MyLogicalExpand

The function by Mathematica to expand a formulation with ANDS, ORS, NOT, XOR, and others, is LogicalExpand, let see an example: ...
1answer
287 views

### GUI of a Karnaugh Map (2)

Adopting kguler's answer to my previous question, I managed to get the simplified map by using Mathematica's build-in function BooleanMinimize. The tough job left ...
0answers
61 views

### Is there a way to make a set of all real numbers within a range? [closed]

Is there a way to create a set of all real numbers within a range? For example, the range between 1300 and 1500, including 1500 in normal distribution. Thank you very much. My problem exactly: $A$ –...
3answers
621 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 ...
3answers
266 views

### Writing code to update a large matrix?

How can I write a code to update a matrix based on certain rules? I plan on constructing a large matrix, and I cannot submit entries one by one. The rules for the matrix are as followed:  P(i,j)=...
1answer
89 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: ...
1answer
73 views

### How to use recursion to find a logical dual

I want to make a little function that goes through a propositional formula and gives it's dual. Here is what I currently have: ...
1answer
765 views

### How would I input this truth table into Mathematica or Wolfram Alpha

I am unsure how to put the negations after a gate or before a gate?
3answers
150 views

### How to limit only two “0 and 1” strings for an xor implement?

I tried to implement some logic gates for a series of "0 & 1" strings, just like and, or, nand, nor and not listed below. How could I limit xor only accept a two strings list as its argument? <...
1answer
546 views

### How to generate the truth table to prove logical equivalence?

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?
1answer
41 views

### Splitting Logical Expression in list of expressions

I have long results of a Reduce statement in the form of {(expr1) || (expr2) || (expr3) || ...} I am looking for a way to split ...
1answer
114 views

### How to do predicate logic in Mathematica

I'm trying to formalize and analyze the following reasoning: All equilateral triangles are isosceles triangles. Some triangles are not equilateral triangles. Therefore some triangles are not ...
1answer
63 views

### What domain does Resolve assume by default?

Consider the statement: $\forall x\left(x<7\Rightarrow \exists a\exists b\exists c(a^2+b^2+c^2=x)\right)$ This is true provided the universe of discourse is $\mathbb{N}$ Now I use ...
1answer
144 views

### Assumptions in mathematica when Symplify on Log[Exp[a/b]]

In mathematica 9.0: This: Assuming[b > 0 || b < 0, Simplify[Log[Exp[a/b]]]] yields: a/b However, this: ...
0answers
36 views

### Solving systems of logial and set theoretic propositions

I need to allocate a couple of dozen elements into different sets, respecting some boundary conditions, and was hoping Mathematica might somehow help. A simple example: The propositions being a) a ...
2answers
155 views

### How to add variables to boolean expression and get conjunctive normal form?

I have the boolean expression (a && !b). I want to add variables c, d into the ...
2answers
64 views

### How to prove that an equation can be divided by any n?

I'm new to Mathematica and came across with the problem. I can't prove that (for example) 2*n is always even no matter what n is....
2answers
129 views

### How may I define e.g. Tilde[x,y] to have certain properties?

I would like to define, e.g., the Tilde[x,y] operator to have certain properties, and then investigate whether certain expressions involving that operator are True or not. For example, if I specify ...
2answers
67 views

### PEANO Integers using successor function

I'd like to define the integers and operations on it by using terms. Starting from zero->init[] and nth->succ[n-1th] where succ[] is the successor function. I ...
1answer
45 views

### Resolving logical statement returns statement as answer instead of boolean value? [closed]

I ran the following command: ...
1answer
48 views

### Resolving a logical statement

I would like to test whether f[n] > 0 and f[n + 1] > 0 implies f[n + 2] > 0. This ...
1answer
249 views

### Testing Equality Expression?

Even if in Graph[{1 -> 2}] == Graph[{1 \[DirectedEdge] 2}] the answer is True ; but why MMA doesn't show the result of the ...
1answer
110 views

### Replace !x with x != 1

I have some logical relationships that I ultimately want to pass to NMaximize as constraints: ...
0answers
53 views

### Function that outputs the dual of the formula

The exercise is simple: define a function that gives the dual of the formula. While I have experience in mathematics and logic, I do not have real experience in programming. Logic is propositional ...
1answer
219 views

### Logic Gates - How to show eight ways an AND function can be realized using negative and postivie logic [closed]

I am asked to use negative and positive logic (using bubbles on the gates) to show eight ways that an AND function can be realized. Im not too sure how to do this. The only way I can create an AND ...