Let R be a relation from Q to Q defined by `R={(a,b): a,b in Q and a-b in Z}`. Show that
(i) `(a,a) in R" for all " a in Q`

Show that * : R xx R to R defined by: a * b =a-5b is not abelian.

Let f: X to Y be a function. Define a relation R in X given by R = {(a,b):f (a) =f (b)}. Examine whether R is an equivalence relation or not.

Show that the relation R in the set Z of intergers given by R ={(a,b):2 divides a-b } is an equivalence relation.

if P,q, r, s in R such that p r= 2 ( q+ s) then

Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a,b):a is sister of b} is the empty relation and R' ={(a,b): the difference between heights of a and b is less than 3 meters } is the universal relation.

Show that **: R x R to R defined by a **b=a + 2b is not commutative.

Let S be the set of real numbers. For a, b in S , relation R is defined by aRb iff |a-b|lt 1 then R is