DM-Sets,Relations and Functions-Q12

+5 votes

Let R denote a relation on the set of all ordered pairs of positive integers by (x,y)R(u,v) if and only if xv=yu. Which of the following is true?

(A). R is a partial order relation

(B). R is an equivalence relation

(C). R is neither partial order relation nor equivalence relation

(D). R is an antisymmetric relation

asked Jul 5, 2019 in Discrete Maths by gbeditor (32,710 points)
reshown Jul 6, 2019 by gbeditor

2 Answers

+3 votes
Best answer

So correct Answer is B

answered Jul 8, 2019 by getgatebook (34,850 points)
selected Jul 9, 2019 by getgatebook
0 votes
B is correct one.
answered Jul 6, 2019 by (34,820 points)
can anyone provide an expalnation, i couldnt visualise because of the ordered pair.
Can you please explain why is it symmetric? for example (1,2) and (2,1)
here,ordered pair present in relation does not contain single elements,instead of that it contains ordered pairs inside of that ordered pair,                                                 for eg.,if relation is {((a,b),(c,d)),((c,d),(a,b))},it is symmetric                                                           since in first pair ,ad=bc                                                                                           second pair also,bc=ad..        
such that both are present in relation and hence it is symmetric.