If R be a relation `lt` from A = {1, 2, 3, 4} to B = {1, 3, 5}, i.e. (a,b) `inRiffaltb`, then `ROR^(-1)`, is

If R be a relation < from A = {1, 2, 3,4) to B = (1,3,5) that is (a, b) in R iff a lt b , then R o R^-1 is

Let A={1,2,3},\ B={1,3,5}dot If relation R from A to B is given by R={(1,3),\ (2,5),\ (3,3)}dot Then R^(-1) is

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

Let R={(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation the set A= {1, 2, 3, 4} . The relation R is (a). a function (b). reflexive (c). not symmetric (d). transitive

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} .

Let A={1,2,3,4} and R be a relation in given by R= (1,1), (2, 2), (3. 3). (4,4), (1,2), (2,1),(3,1), (1,3)} . Then R is

Let R be the equivalence relation in the set A={0,1,2,3,4,5} given by R={(a ,b):2d i v i d e s(a-b)}dot Write the equivalence class [0].

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 .

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}.