Recent questions tagged relations

Define $\mathcal{R}$ the binary relation on $\mathbb{N} \times \mathbb{N}$ to mean $(a, b) \mathcal{R}(c, d)$ iff $b \mid d$ and $a \mid c$$\mathcal{R}$ is symmetric but ...

Let $A$ be any set. Subset Relation on $\mathrm{P}(\mathrm{A})$ is Anti-symmetric?

Define $\mathcal{R}$ the binary relation on $\mathbb{N} \times \mathbb{N}$ to mean $(a, b) \mathcal{R}(c, d)$ iff $b \mid d$ and $a \mid c$

Consider the following binary relations on the naturals (non-negative integers). Which ones are reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify ...

The relation $\mathcal{R}$ on $\mathbb{Q}$ with $\forall x, y \in \mathbb{Q}: x \sim y$ if $x y=0$.The relation "has the same mother" on the set of students.The relation ...

Are the following relations reflexive, symmetric, transitive, antisymmetric? Explain.Let $R$ be a relation on $\mathbb{Z}$ such that $(a, b) \in R$ iff $b=a$ or $b=-a$.Le...

Let $A \neq \varnothing$ be a set. Consider the following statements:$\varnothing$ is a reflexive binary relation on $A$;$\varnothing$ is a symmetric binary relation on $...

Define the binary relation $R$ on the set $A:=\{-4,-3,-2,-1,1,2,3,4\}$ as follows:$$(x, y) \in R \Longleftrightarrow\left|x^2-y^2\right| \leqslant 5$$for all $x, y \in A$...

$$R=\left\{(x, y) \in \mathbb{N}^2: \exists n \in \mathbb{N}, x^n=y\right\}$$is a binary relation on the set of natural numbers $\mathbb{N}$.Determine which of the follow...

Determine if each of the following relations is reflexive, symmetric, antisymmetric, or transitive. Indicate if the relation is an equivalence relation.$R_1=\{(a, b) \mid...

Let $R \subseteq \mathbb{N} \times \mathbb{N}$ be a relation ( $a$ binary relation) on the set of natural numbers defined as follows:$$(x, y) \in R \Leftrightarrow x+y \g...

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is both reflexive and symmetricIt is only reflexive...

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is both symmetric and transitiveIt is both reflexiv...

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is only reflexiveIt is reflexive, symmetric, and tr...

Among reflexive, symmetric, antisymmetric, and transitive, which of those properties are true of the above relation?It is only transitiveIt is both antisymmetric and tran...

Let $R$ be the relation on $M=\{1,2,3\}$ with the following diagraph representation:Then$R$ is not reflexive, not symmetric, and not transitive$R$ is transitive but not r...

Define the relation $\mathrm{O}$ on $\mathrm{Z}$ as follows:$$\forall m, n \in Z, m O n \longleftrightarrow \exists k \in Z \mid(m-n)=2 k+1$$Which one of the following st...

For each of the following relations $R$ on the set of real numbers, decide whether it is reflexive, symmetric, and/or transitive? Justify your arguments. Is the relation ...

 A relation '$R$ ' is defined on ordered pairs of integers as: $(x, y) R(u, v)$ if $x<u$ and $y>v$. Then $R$ isNeither a partial order nor an equivalence relationA partia...

Identify the incorrect statement(s).A candidate key is minimal set of one or more attributes that, taken collectively, allows us to uniquely identify any entity in the en...

Consider the two relations below. The primary keys are underlined. Identify all possible foreign key(s) from the options based only on the two relations.$\text{EMP (eid, ...