A binary relation R in the set `A={2,3,4,5,6}` is defined by xRy, where `|x-y|` is divisible by 3. Is R an equivalence relation?

Show that the relation R in the set A={x in Z:0lexle12} given by R={(a,b):|a-b|" is multiple of "4} is a equivalence relation. Find the set of all elements related to 1.

Define a relation in the set A={1,2,3,4} which is transitive but not symmetric.

Show that the relation R in the set Z of integers given by R{(x,y):6" divides "x-y} is an equivalence relation. Find the set of all elements related to 0.

Given an example of an empty relation in the set A={1,2,3,4} .

Let R be the relation defined in the set A={1,2,3,4,5,6,7,8,9} 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 lements of the subset {1,3,5,7,9} are related to one another and all the lement of the subset {2,4,6,8} are related to one another but no element of the subset {1,3,5,7,9} is related to any element of the subset {2,4,6,8} .

Show that the relation R in the set of integers given by R={(a,b):4" divides "a-b} is an equivelence relation. Find the set of all elements related to 0.

Give an example of a universal relation in the set A={1,2,3,4} .

Let N be the set of all natural numbers and R be the relation in NxxN defined by (a,b) R (c,d), if ad=bc. Show that R is an equivalence relation.

If R={(1,2),(2,3)} is a relation in N, list the least number of ordered pairs to be included in R so that R is an equivalence relation.