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20
votes
1answer
486 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 ...
10
votes
2answers
445 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
125 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
154 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
71 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
712 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 ...
2
votes
2answers
246 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, ...
2
votes
1answer
82 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
0answers
157 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
257 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
167 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
1answer
111 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
117 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
50 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
56 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
106 views

Replace !x with x != 1

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

Is mathematica able to count all results?

I have N variables, say $V_1, V_2, ..., V_n$. and I have several logical conditions like $[(V_1 > V_2) \cap (V_2 + V_3 > V_1) \cap (V_1*V_1 > 2*V_2)] \cup [..]$ You can consider they are in ...
-1
votes
1answer
80 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 ...