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20
votes
1answer
526 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 ...
14
votes
4answers
1k 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) ...
10
votes
2answers
592 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 ...
5
votes
2answers
147 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 ...
5
votes
2answers
198 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 ...
5
votes
0answers
80 views

Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite ...
4
votes
3answers
995 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 ...
3
votes
2answers
304 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, ...
3
votes
2answers
123 views

TrueQ returning False on true statement

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

Make MyLogicalExpand

The function by Mathematica to expand a formulation with ANDS, ORS, NOT, XOR, and others, is LogicalExpand, let see an example: ...
2
votes
1answer
229 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 ...
2
votes
0answers
196 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!
1
vote
3answers
339 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 ...
1
vote
1answer
166 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?
1
vote
3answers
116 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? ...
1
vote
1answer
300 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?
1
vote
2answers
40 views

Logical expression evaluations [closed]

Why TautologyQ[Equivalent[Implies[p, And[q, r]], And[Implies[p, q], Implies[p, r]]]] is True and ...
1
vote
1answer
54 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 ...
1
vote
1answer
128 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: ...
0
votes
2answers
127 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 ...
0
votes
2answers
47 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 ...
0
votes
2answers
77 views

Alternative to xor(A,B,C) [closed]

How can we make a comprehensive statement, which will correspond to the truth table of xor (A, B, C) (means that only true if exactly one of A,B,C is true) by combining logical operators AND (&), ...
0
votes
1answer
96 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 ...
0
votes
1answer
109 views

Replace !x with x != 1

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

Is it possible to simulate a RS latch?

Combining the solutions provided from the nice guys here to my previous two questions(first, second), Interesting enough, simulations for simple logic gates can be implemented easily. An example is ...
-1
votes
1answer
94 views

Transformation of a simple logic statement

I'm designing a logic circuit and I was wondering if the following two things are equivalent: (x <= y) and (x < (y + 1)) I can't think of any set of numbers that would make these two things ...