# Tagged Questions

For questions about the algebra used for modeling the data stored in relational databases.

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### Why study graph representations of equivalence relations?

What is the importance of representing a (an equivalence) relation using digraphs? Is there any geometric aspect to study relations using graphs (of vertices and edges)?
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### Is it possible that $(\text{even}/\text{even})\times \text{even} = \text{odd}$? [closed]

Do even natural numbers $e_1,e_2,e_3$ exist with $\frac{e_1}{e_2}\cdot e_3=o$, such that $o$ is an odd natural number? Find a relation for these three even numbers $(e_1,e_2,e_3)$.
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### Number of possible ways to join n relations

The number of possible ways to join n relations r1⨝r2⨝r3.....⨝rn can have 3 distinct cases - If the join orders cannot change i.e. ri can only be joined to rj or any other intermediate relation ...
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I am confused about this notation from the image below. How can you represent something like (1,2),1 as a 2D matrix? For S1 = (0,1,2) and S2 = (0,1) I would expect two matrices like: [(1,0),(1,0),...
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### Source proof of equivalence between relation algebra and three variable first order logic

I am reading up on relation algebra and a lot about first order logic. Being a bit of a heavy torsion on the latter one as I am not used to it. Either way I read on wikipedia that up to 3 variable ...
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### Complexity of Yannakakis Algorithm

I've been independently studying database theory, and I've recently learned about Yannakakis algorithm, a technique for performing acyclic joins. I've read several different explanations, and they all ...
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### Relational Algebra Find Tuple in Every Group

I am having trouble with some Relational Algebra problems Namely how to select a tuple that appears in every grouping I know how to deal with this in SQL but have trouble solving the following ...
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### Can a tuple be defined as an instance of a relationship?

SO let's say x and y are in relation. Is (x,y) a tuple and an instance of a relation ? Is a n-tuple an instance of a n-relation?
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### why does the relational algebra not allow duplicates?

unlike SQL, duplicate rows are automatically eliminated.. $\delta(R)$ will result in the elimination of duplicate tuples, but what is the reason for this?
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### How to find who are those that have never return a book late in relational calculus?

Let's assume that the Congress library has a database with the following pattern (the primary keys are in bold) Borrowing(People, Book, DateBorrowing, ExpectedReturnDate, EffectiveReturnDate) ...
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### How to find in relational calculus which people likes at least and exactly two topics?

A relational database has the following relations: Likes(People,Topic), Study(People, Topic), ...
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### Relational Aglebra, dont know what to do!

The following relational tables/schemes are given: In bold is the primary key, in Italics is foreign key: -City(Name,Country,Population) -Venue(VID,Capacity,Name) -Concert(KID,ID,DID,duration) -...
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### E1 and E2 are equivalent then they are “almost equivalent”

Given : 2 statements E1, E2 in relational algebra are "almost equivalent" if every phase in the database D ,except finite number of D's E1(D)=E2(D). E(D) means the result of activating the statement E ...
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### Proving equivalence relation for 7 | (3a + 4b)

I know this might be quite trivial, but I just can't seem to figure out how to prove $$R = \{(a,b) \in \mathbb{Z} \times \mathbb{Z} : 3a + 4b \text{ is divisible by } 7\}$$ is a symmetric relation, i....
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### Converting between relational calculus and relational algebra

So I'm trying to get my head around relational algebra and calculus and converting between them. I understand that... $$\{ x\mid\exists y.F(x,y) \wedge G(x,y)\}$$ ...equates to $\pi_A F \cap G$ But ...
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### Relational Database Reductions

So In the study guide for our Db Design final, the professor gave us this Information preserving logical design, Where bold is a primary key and italics are a foreign key. L1: Donor: D_ID, D_Name, [...
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### 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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### Forward and backward composition in relational algebra

Forward composition: $p\,;q$ $$\forall p,q\cdot p\in S\leftrightarrow T\land q\in T\leftrightarrow U\implies\\p\,;q=\{x\mapsto y\mid(\exists z\cdot x\mapsto z\in p\land z\mapsto y\in q)\}$$ ...
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### 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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### 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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### 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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### “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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### 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 ...