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Proving that A ∩ B subset of C <-(if and only if)-> A is subset of complement of B union C (Set theory) [migrated]

I'm trying to prove the following statement: I need to do it using a formal proof.. I've tried to do it for some time now and couldn't find anything close.. Thanks!
5
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1answer
136 views

How is LHS = RHS; … ; RHS (nontrivially) different from … ; RHS

I'm trying to understand how Mathematica thinks about the results of Set. Suppose we perform LHS = RHS. I'm focusing on when ...
4
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1answer
71 views

Problem with Simplify, Sqrt, and Set: What's going on?

I am having some trouble getting Mathematica to simplify an expression of the form Sqrt[x]*Sqrt[1/x], where x>0. The problem is that x is assigned to some complicated form by the time Mathematica ...
3
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1answer
86 views

Finding pairs where the intersection of them is empty set from a nested list

It would be better to give an example first. Suppose I have a nested list of the form list = {{ 1,2,3,6}, { 3,6,10,20}, { 4,7,11}, { 10,20}}; where each element ...
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1answer
173 views

Why can AppendTo modify a referenced list in-place but Part cannot?

Part, AppendTo, PrependTo, AddTo, etc. allow in-place modification of a list, but only Part requires that the list be referenced through a simple symbol, e.g. the following all does what you'ld ...
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3answers
135 views

Finding largest Range in a list

In a list of positive integers, I would like to find the largest n such that Range[n] is a subset of the list. So for example ...
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0answers
15 views

Difference Equation System constructed with SetDelayed: How I can set Non-exploding break?

I have a Difference Equation System constructed with SetDelayed. The system is like as follow. ...
5
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1answer
234 views

A more perfect Union[]

I was doing a Project Euler problem with my class, and found the following weird fact: Union[] of a list of some 50 million numbers (of which only around 15000 were ...
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2answers
205 views

Modifying parameters: Set::setps in the part assignment is not a symbol [duplicate]

Ok, this will probably be a silly question, but I can't get my head around it. I'm making a simple module that, given a list and two integers, will swap the position of the elements in the ...
3
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1answer
67 views

How can I create a set (list) provide a kind of rule/algorithm?

Example: S = {r ∈ Q : r² < 2} Let S be the set of all rational numbers whose squares are less than 2. It follows that 1 ∈ S, 4/3 ∈ S, but 3/2 doesn't ∈ S because 9/4 ≥ 2. Thank you.
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3answers
277 views

Implementing key-value associations in Mathematica 9 with inexact numbers for keys

I'm not sure of what type of problem my issue falls into, so I haven't been able to search forums with any success. If this has already been solved then my apologies! Essentially I'm trying to set a ...
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96 views

Is there a better way of creating/assigning variables programmatically than using strings and ToExpression?

For quite a while now I've been wondering how to assign variables programmatically, and I have finally figured out one way of doing this. For example in a game where you have a variable number of ...
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57 views

Set-generating macro unexpectedly reaches recursion limit

One moment I decided to assign symbolic names to all special spaces since they all look the same when put literally in FrontEnd editor, more or less like "" or ...