# Recent questions tagged relations

1
A relation $R$ is said to be circular if $aRb$ and $bRc$ together imply $cRa$. Which of the following options is/are correct? If a relation $S$ is reflexive and symmetric, then $S$ is an equivalence relation. If a relation $S$ is circular and symmetric, ... and circular, then $S$ is an equivalence relation. If a relation $S$ is transitive and circular, then $S$ is an equivalence relation.
2
Consider the following properties: Reflexive Antisymmetric Symmetric Let $A=\{a,b,c,d,e,f,g\}$ and $R=\{(a,a), (b,b), (c,d), (c,g), (d,g), (e,e), (f,f), (g,g)\}$ be a relation on $A$. Which of the following property (properties) is (are) satisfied by the relation $R$? Only $a$ Only $c$ Both $a$ and $b$ $b$ and not $a$
3
What is the possible number of reflexive relation on a set of $5$ elements? $2^{10}$ $2^{15}$ $2^{20}$ $2^{25}$
4
The relation $\{(1,2),(1,3)(3,1),(1,1),(3,3),(3,2),(1,4),(4,2),(3,4)\}$ is Reflexive Transitive Symmetric Asymmetric
5
Let $R$ and $S$ be two fuzzy relations defined as: $\begin{matrix} & & & &y_1& &y_2\end{matrix}\\R=\begin{matrix}x_1\\x_2\end{matrix}\begin{bmatrix} 0.6 &0.4 \\ 0.7&0.3 \end{bmatrix} \text{ and}$ ...
1 vote
6
What will be solution of recurrence relation if roots are like this: r1=-2, r2=2, r3=-2, r4=2 is this the case of repetitive roots?
7
What is the covering relation of the partial ordering {(A, B) | A ⊆ B} on the power set of S, where S = {a, b, c}? i'm getting R={(Ф, {a}), (Ф, {b}), (Ф, {c}), (Ф, {a, b}), (Ф, {b, c}), (Ф, {a, c}), (Ф, {a, b, c}), ({a}, {a, b}), ({a}, {a, c}), ({b}, {b, c}), ({b}, {a, b}), ({c}, { ... {a, b}), ({b}, {b, c}), ({c}, {a, c}), ({c}, {b, c}), ({a, b}, {a, b, c}), ({a, c}, {a, b, c})({b, c}, {a, b, c})
8
Suppliers(sid, sname, address) Parts(pid, pname, color) Catalog(sid, pid, cost) Find the pids of the most expensive parts supplied by suppliers named Yosemite Sham
9
Given relation catalog(sid, pid, cost) Find pairs of sids such that the supplier with the first sid charges more for some part than the supplier with the second sid what is the relational algebra expression for this?
10
What is dual of a POSET?
11
Suppose that $A$ is a nonempty set, and $f$ is a function that has $A$ as its domain. Let $R$ be the relation on $A$ consisting of all ordered pairs $(x, y)$ such that $f (x)=f (y)$ $a)$ Show that $R$ is an equivalence relation on $A$ $b)$ What are the equivalence classes of $R?$
12
For each part, give a relation that satisfies the condition. Reflexive and symmetric but not transitive Reflexive and transitive but not symmetric Symmetric and transitive but not reflexive
Given two relations R1 and R2, where R1 contains N1 tuples, R2 contains N2 tuples, and N2>N1> 0, give the minimum and maximum possible sizes (in tuples) for the result relation produced by each of the following relational algebra expressions. In each case, state any assumptions about ... difference) $R1 X R2$ (cartesian product) $σa=5(R1)$ (selection) $\pi a(R1)$ (projection) $R1/R2$ (division)
R is iff $R ^{-1}$ is Total ? a function ? a surjection ? an injection ? a bijection ? Fill in the entries in the table.