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

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

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

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}.

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}.

Check whether the relation R defined on the set A={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.

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

If R is a relation on the set A={1,2,3} given by R={(1,1),(1,2),(2,1)} , then R is

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 divisible by 2} is an equivalence relation. Write all the equivalence classes of R .