Show that the relation `R` on the set `A={x in Z ;0lt=xlt=12}` , given by `R={(a ,\ b): a=b}` , is an equivalence relation. Find the set of all elements related to 1.

Show that the relation R on the set A{xZ ;0lt=12}, given by R={(a , b): a=b}, is an equivalence relation. Find the set of all elements related to 1.

Show that the relation R on the set A={x in Z :0lt=xlt=12} , given by R={(a ,\ b):|a-b| is a multiple of 4} is an equivalence relation. Find the set of all elements related to 1 i.e. equivalence class [1].

Show that the relation R on the st A={ xin Z:0lexle12} , given by R={a,b),|a-b| is multiple of 4} is an equivalence relation.

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

Show that the relation S in the set A={x\ \ Z\ :0\ lt=x\ lt=12} given by S={(a , b):\ a ,\ b\ \ Z ,\ \ |a-b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1.

Show that the relation R on the set A={1,\ 2,\ 3,\ 4,\ 5} , given by R={(a ,\ b):|a-b| is even }, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But, no element of {1, 3, 5} is related to any element of {2, 4}.

Prove that the relation R in set A = {1, 2, 3, 4, 5} given by R = {(a,b): |a-b| is even} is an equivalence relation .

Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a , b) : |a - b| is e v e n} , is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4 } are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4} .

If R is an equivalence relation on a set A, then R^-1 is