Question

2) [60pts] Let A be a non-empty set. Consider the set of all relations on A and call it $\mathcal{R}_A$. Now consider the relation $\Psi$ on $\mathcal{R}_A$ that is defined as $\forall x, y \in A \ \forall R_1, R_2 \in \mathcal{R}_A \ R_1 \Psi R_2 \iff [xR_1y \implies xR_2y] \text{ }$. Prove that the relation $\Psi$ on $\mathcal{R}_A$ is an order relation.

Name: 2) [60pts] Let A be a non-empty set. Consider the set of all relations on A and call it ℛA. Now consider the relation Ψ on ℛA that is defined as ∀ x, y ∈ A ∀ R1, R2 ∈ℛA R1 Ψ R2 [xR1y xR2y]. Prove that the relation Ψ on ℛA is an order relation.
Uploaded: 2023-08-10T05:20:09-08:00
Duration: 5 min 38 s
Channel: Madhur L
Description: 2) [60pts] Let A be a non-empty set. Consider the set of all relations on A and call it ℛA. Now consider the relation Ψ on ℛA that is defined as ∀ x, y ∈ A ∀ R1, R2 ∈ℛA R1 Ψ R2 [xR1y xR2y]. Prove that the relation Ψ on ℛA is an order relation.

          2) [60pts] Let A be a non-empty set. Consider the set of all relations on A and call it $\mathcal{R}_A$. Now consider the relation $\Psi$ on $\mathcal{R}_A$ that is defined as $\forall x, y \in A \ \forall R_1, R_2 \in \mathcal{R}_A \ R_1 \Psi R_2 \iff [xR_1y \implies xR_2y] \text{ }$. Prove that the relation $\Psi$ on $\mathcal{R}_A$ is an order relation.

2) [60pts] Let A be a non-empty set. Consider the set of all relations on A and call it ℛA. Now consider the relation Ψ on ℛA that is defined as ∀ x, y ∈ A ∀ R1, R2 ∈ℛA R1 Ψ R2 [xR1y xR2y]. Prove that the relation Ψ on ℛA is an order relation.

Added by Tina T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/10/2023

Step 1

Step 1: To prove that $\Psi$ is an order relation, we need to show that it is reflexive, antisymmetric, and transitive. Show more…

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2) [60pts] Let A be a non-empty set. Consider the set of all relations on A and call it $\mathcal{R}_A$. Now consider the relation $\Psi$ on $\mathcal{R}_A$ that is defined as “$\forall x, y \in A \ \forall R_1, R_2 \in \mathcal{R}_A \ R_1 \Psi R_2 \iff [xR_1y \implies xR_2y]$”. Prove that the relation $\Psi$ on $\mathcal{R}_A$ is an order relation.