Answer to Question #282231 in Discrete Mathematics for Aman

Question #282231

R= {(1,3) ,(1,4) , (3,2) , (3,3), (3,4)} on A={1,2,3,4}


1
Expert's answer
2021-12-24T04:59:49-0500

Question is incomplete.

Let us take an example related to the given problem:

Let R= {(1,3) ,(1,4) , (3,2) , (3,3), (3,4)} be a relation on set A={1,2,3,4}. Then relation R is?

Answer:

R= {(1,3) ,(1,4) , (3,2) , (3,3), (3,4)}

It is seen that (a,a)R(a,a)\notin R , for every a{1,2,3,4}.a∈\{1,2,3,4\}.

∴ R is not reflexive.

It is seen that (1,3)R(1,3)∈R , but (3,1)(3,1) \notin R.

∴ R is not symmetric.

Also, it is observed that (a,b),(b,c)R(a,c)R for all a,b,c{1,2,3,4}(a,b),(b,c)\in R⇒(a,c)\notin R\text{ for all }a,b,c∈\{1,2,3,4\}

∴ R is not transitive.

Hence,R neither is reflexive nor transitive nor symmetric.


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