Let the relation R be defined on the set
`A={1,2, 3,4,5}" by "R={(a, b):abs(a^(2)-b^(2)) lt 8}:` Then R is given by ........... .

Let R be the relation defined on the set : A= {1, 2, 3, 4, 5,.6, 7} by: R ={(a, b) : a and bare either odd or even}. Show that R is an equivalence relation.

Check whether the relation R defined in the set {1, 2,3,4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

Let R be the relation defined in 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}.

The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R^(-1) is given by

Check whether the relation R defined in the set (1, 2, 3, 4, 5, 6) as R= {(a, b) : b = a +1)} is reflexive, symmetric or transitive ?

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 5 divides abs(a-b)} is an equivalence relation.

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 4 divides abs(a-b)} is an equivalence relation.