"Let `R` be the relation defined on the set `A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}` by `R={(a ,\ b):`
Channel: Doubtnut
Date: 2020-06-28

"Let `R`
 be the relation defined on the set `A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}`
 by `R={(a ,\ b):`
 both `a`
 and `b`
 are either odd or even}. Show that `R`
 is an equivalence relation. Further, show that all
 
  the elements of the subset {1, 3, 5, 7} are related to each other and all the
 
  elements of the subset {2, 4, 6} are related to each other, but no element of
 
  the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}."