Show that the relation `R` in the set `A = {1, 2, 3, 4, 5}` given by `R = {(a, b) : |a – b|` is divisible by `2}` is an equivalence relation. Write all the equivalence classes of `R`.

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} .

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 .

The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b): |a^(2)-b^(2)|lt16} is given by

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}.

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={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 defined by R={(a , b):a-b is divisible by 3; a , bZ} is an equivalence relation.

Show that the relation R defined by R={(a , b):a-b is divisible by 3; a , bZ} is an equivalence relation.

Show that the relation R defined by R={(a , b):a-b is divisible by 3; a , bZ} is an equivalence relation.

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.