632 views
1 votes
1 votes

A binary relation R on Z × Z is defined as follows:
                                                        (a, bR (cd) iff a = c or b = d
Consider the following propositions:
1. R is reflexive.                                       2. R is symmetric.
3. R is antisymmetric.
Which one of the above statements is True?

2 Answers

0 votes
0 votes
I think it is an equivalence relation ( reflexive,anti symmetric and symmetric), since

if  (a,b)=(1,2) and (c,d)=(1,8)

so one condition is true for relation i.e. a=c  so R= { (1,1) }

and it is reflexive, anti-symmetric and symmetric since in anti -symmetric diagonal pairs are allowed.

 

Please correct me if I am wrong.

Related questions

1 votes
1 votes
1 answer
1
Aditya Bahuguna asked Jan 4, 2018
375 views
1 votes
1 votes
2 answers
2
Aditya Bahuguna asked Jan 3, 2018
369 views
0 votes
0 votes
1 answer
3
Abhipsa asked Jan 23, 2019
533 views
What is the number of relations S over set {0,1,2,3} such that (x,y) $\epsilon$ S $\Rightarrow x = y$ ? Thanks.
0 votes
0 votes
0 answers
4
Kanaga asked Sep 20, 2018
189 views
Check if r is reflexive ,transitive,symmetric arb for 1+ab