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How do I find a particular set of records using relational algebra operations?

Suppose I have the following relation C. c1 | c2 a | a a | b b | a b | b If I do \select_{c1 != c2}C, I get the pairs (a,b) and (b,a). But for my purpose, they are same. So I would like to ...
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29 views

Does R(5,7) hold or not in this relation?

This is the question: Let $A=\{1,...,7\}$ and let $R\subseteq A\times A$ be a relation which is symmetric and transitive. You have been given some partial information about the relation which is ...
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0answers
8 views

How to create a total order of a set of triplets

I have a set $ M = \{a_1,...,a_n\} $ where every $a$ is a triplet $ a = (x,y,z) $. I know want to do some things with this. I want to build a set $ N \subseteq M $ which contains all triplets that ...
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1answer
50 views

fastest and most efficent way to count all combinations in many sets and sum them together

I am a Java programmer who has reached the limits of brute computer power. My relational database (and non relational databases) is not producing results quick enough and I have hit a bottleneck in ...
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0answers
9 views

Optimization of a set-based invariant for a single element case

As I understand it, various algebras have useful identities. For example, in boolean algebra, !a & !b is equivalent to ...
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1answer
22 views

Relational Algebra : Cross Product of a Relation with Table-Dum & Table-Dee

I am wondering what would be the result of the following operation: Let $A$ be a relation with $n$ ($n > 0$) attributes and $t$ ($t > 0$) tuples. Let $TableDum$ be a relation with $0$ ...
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1answer
21 views

Functional dependency - adding any attribute to X will still yield a FD?

I have heard my professor saying that when X → Y is a functional dependency, adding any attribute to X or removing any attribute from Y will still yield a functional dependency. I do not understand ...
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22 views

Expressing relational algebra queries in plain english

This statement: And this one: How do I go about converting these to plain english? Here is the extent of my understanding: For the first one, I think it's selecting p_id where there exists ...
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1answer
65 views

Difference between $A\to B\to C$ and $A\to(B\to C)$

As the title says, what is the difference between $A\to B\to C$ and $A\to(B\to C)$? I have tried to reduce these expressions into $A\to B === (A\text{ OR } \text{NOT} B)$ form but didn't get anywhere. ...
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1answer
50 views

Help solving a challenge - relational algebra or second order logic

I am a self-taught man and I'm posting my first question here. I'm facing a challenge I'd like to solve. Based on what I know it fits propositional calculus (hope it is). Suppose 3 people: a ...
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3answers
65 views

How did I solve this problem?

While writing a SQL query I had to solve a problem I'd never dealt with before. It was trivial, but I cannot explain the solution without drawing lines on paper or making examples with actual numbers ...
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1answer
62 views

Proof - Projection distribution over set union

I've just started databases and have exercise to proof that projection$(\pi)$ is distributive over set union$(\bigcup)$. But I suck in proofs and don't really know how to proof that: $\pi_\alpha( R ...
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1answer
55 views

Relational Algebra: Showing equality using aggregate operator

The schemas are given here for relations $R$ and $S$: $$R(A,B)$$ $$S(C,D,E)$$ One can see that the following equality is true: $$\gamma_{B,sum(E)}(R\Join_{A=C}S) = \gamma_{B,sum(E)}(R\Join_{A=C} ...
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58 views

Need review of Relational Algebra

These are technically homework but I'd like to have verified whether what I did is right or wrong, so I don't upright ask for a solution at least. • Find the names, street address, and cities of ...
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14 views

How do I express join conditions on two unnamed relations using relational algebra?

Let's say I have three relations: $instructors$ who teach classes, $classes$ that are taught, and $attends$, a relationship between classes and the students who attend them. The relations have the ...
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1answer
67 views

Forward and backward composition in relational algebra

http://imgur.com/lMbx4Q5 I am having trouble understanding what forward composition and backward composition mean. The picture above is from my unit notes and I just fail to see any intuition reading ...
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1answer
27 views

Equivalence between relational algebra statements

This is a practice question for a relational algebra question which I don't understand. Consider two relations $R(A, B)$ and $S(B,C)$. Which of the following relational algebra expressions is not ...
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1answer
105 views

Relational Algebras and Relational Calculus

Suppose we have a statement $S$ such as "The number of people connected to Bob through any number of friends." Why is this statement expressible in relational algebra but not in relational calculus? ...
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92 views

How to denote the set of binary relations of which a particular ordered pair is a member?

Given a universe $U$ and two subsets $S$ and $T$ (also, both members of $U$), what is the name given to denote the set of all binary relations in $U$ where the ordered pair $(S,T)$ is a member? The ...
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2answers
69 views

“Het” ternary and n-ary relations in $\bf Rel$?

Are n-ary relations, with n > 2, in $\bf Rel$ - the category of sets as objects and relations as arrows? By "het" (heterogeneous) relations I mean relations between distinct sets, so $X \to Y$, as ...
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1answer
95 views

Relations as arrows and as objects - what are the arrows in the latter?

Since a relation $R$ from $X$ to $Y$ defined as a subset of $X \times Y$, the category of sets and relations is just that: the objects are sets and the arrows are the relations. Is there a generally ...
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1answer
62 views

In relational algebra, what would be the result of $(R-S)\cup (S-R)?$

Suppose relation $R(A,B,C)$ has the following tuples: $X\;\;\;\; Y\;\;\;Z$ $1\;\;\;\;\; 2\;\;\;\;\; 3$ $4\;\;\;\;\; 2\;\;\;\;\; 3$ $4\;\;\;\;\; 5\;\;\;\;\; 6$ $2\;\;\;\;\; 5\;\;\;\;\; 3$ ...
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2answers
526 views

Distinguishing equality and isomorphism as relations

Is this relational characterization of equality in Wikipedia accepted? The identity relation is the archetype of the more general concept of an equivalence relation on a set: those binary ...
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0answers
141 views

Example relations: pairwise versus mutual

There are by now several questions on math.se asking about pairwise versus mutual relations, eg: • When does “pairwise” strengthen and when does it weaken? • Relation: pairwise and mutually • ...
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1answer
98 views

Categories of $n$-ary relations?

Arrows in the category $\bf Rel$ are binary (2-valued) relations between set objects. Do ternary, 4-term, $n$-term and variadic (2-valued) relations form categories? (Or perhaps one category?). It ...
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1answer
51 views

Category of Pointed Relations

There are the categories $\mathbf{Set}$ and $\mathbf{pSet}$; given the category $\mathbf{Rel}$, can we define an analogous category $\mathbf{pRel}$ as well? A relation $R \subseteq A \times B$ is said ...
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0answers
70 views

wikipedia relation algebra example #3

Wikipedia article gives the following relation algebra example: 3 An important generalization of the previous example is the power set $2^E$ where E ⊆ X² is any equivalence relation on the set X. ...
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1answer
265 views

Motivation behind Theory of Relations?

I looked through the nice paper by Tarski On the Calculus of Relations. In the beginning he touched a motivation behind Theory of Relations but this part was not clear to me (page 1, very beginning): ...
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2answers
301 views

Functional dependencies A->B and C->B, but not AC->B?

If I have a relation: A B C 1 2 3 4 5 6 7 2 8 Where $A\mapsto B$ and $C \mapsto B$. Doesn't that mean that $AC \mapsto B$? How can you even have this relation? ...
2
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1answer
169 views

What does Tarski mean by a “tautological operation” on a Boolean algebra?

I am reading Part II of Chin and Tarski's "Distributive and Modular Laws in the Arithmetic of Relation Algebras". In the beginning of section 4, the authors say "In general, if $\odot$ is a binary ...
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1answer
208 views

What does it mean for a relation algebra to be simple?

I am reading "Boolean Algebras with Operators part II" by Bjarni Jonsson and Alfred Tarski. On theorem 4.10 (p.132-133), they refer to a relation algebra $\mathfrak{A}$ being "simple" and proves that ...
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2k views

Equivalence Relations and Inverse Relations

Prove that if $R$ is an equivalence relation on a set $A$, then $R^{-1}$ is also an equivalence relation on $A$. Solution: We know that $\forall R\in A$, $$ R = \{(a, b) | (b, a)\in A\} $$ ...
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1answer
695 views

Software for testing relational algebra

Does anyone know of any software to let you test relational algebra queries? By this I don't mean a database such as MySQL, something where the query can be input in some for of mathematical notation ...
3
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1answer
199 views

What is the “Boolean algebra fragment of RA”?

The Wikipedia article on Relation Algebra notes that this is a formal system which has essentially the same expressive power as the three-variable fragment of first-order logic. Peano Arithmetic can ...
3
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2answers
113 views

Where can I find good information, tutorials and or examples on relational algebra queries?

Taken a break from my personal project and getting some work done. I would like to find some examples, tutorials on relation algebra. Anything with good examples will be very useful