Recent questions tagged partial-order

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason RAssertion A: Let $\mathrm{R} \subseteq \mathrm{A} \times \mathrm{A}$ b...

Consider the poset ({3,5,9,15,24,45},|). Which of the following is correct for the given poset? A. There exists a least element but not a greatest elementB. There exists ...

Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows\[P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\}\]The number of total orders ...

Let $A$ be the set of all ordered pairs of integers, that is, $A=Z \times Z$. Define a binary relation $R$ on $A$ as follows: for all $(a, b),(c, d) \in A$,$$(a, b) R(c, ...

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

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

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...

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...