Solution to R3 = {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4), (3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)} Determine whether the relation R3 is reflexive, symmetric, anti-symmetric and transitive. … - Sikademy
Author Image

Archangel Macsika

R3 = {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4), (3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)} Determine whether the relation R3 is reflexive, symmetric, anti-symmetric and transitive. Determine whether the relation R3 is an equivalence relation or partial order. Give reason for your answer

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

Consider the relation R_3 = \{\ (1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4), \\ (3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)\ \}on the set A=\{1,2,3,4\}.

  1. Since (a,a)\in R_3 for each a\in A, the relation R_3 is reflexive. Taking into account that (a,b)\in R_3 implies (b,a)\in R_3 for any pair (a,b)\in R_3, we conclude that the relation R_3 is symmetric. Since (1,2)\in R_3 and (2,1)\in R_3, this relation is not anti-symmetric. Taking into account that (a,b)\in R_3 and (b,c)\in R_3 implies (a,c)\in R_3 for any pairs (a,b),(b,c)\in R_3, we conclude that the relation R_3 is transitive.
  2. Since the relation R_3 is reflexive, symmetric and transitive, it is an equivalence relation. Taking into account that R_3 is not anti-symmetric, we conclude that R_3 is not a partial order.

Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-1446-qpid-1184