Answer to Question #148109 in Discrete Mathematics for Promise Omiponle

Question #148109
Let S be a finite non-empty set. How many relations on S are simultaneously an equivalence relation and a partial order? Justify your answer.
1
Expert's answer
2020-12-11T10:49:23-0500

Let "R\\subset S\\times S" be a relation that is simultaneously an equivalence relation and a partial order, that is "R" is reflexive, transitive, symmetric and antisymmetric. Since "R" is reflexive, "(x,x)\\in R" for any "x\\in S." Let "(x,y)\\in R". Since "R" is symmetric, we conclude that "(y,x)\\in R". Taking into account that "R" is antisymmetric and "(x,y)\\in R, \\ (y,x)\\in R" , we conclude that "y=x." Therefore, "R=\\{(x,x)\\ |\\ x\\in S\\}" is the unique relation.


Answer: 1



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS