Let A={1,2,3,4,5,6}.Define a realtion R from to A by R={(x,y):y=x+1}`.Depicit this relation using an arrow diagram.

R is a relation in the set A={1,2,3,…..,15} such that R={(x,y):y=3x} .Find the domain and range of R.

Let A={1,2,3,4}, B={2,4,6,8} . If f : A rarr B is defined by f(x)=2x , show that (f^-1)^-1=f

Given the sets A = {1,2, 3, 4, 5} and B = {1, 3, 5}, write R as a set of ordered pairs, if the relation R from A to B is defined by ‘x isless than y’. State the domain and the range of the relation

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} .

Let A={1,2,3} , For x, y inA , let xRy if and only if xgty . Write down R as a subset of AxxA .

Let f{(x,(x^2)/(1+x^2):x in R} be a function from R into R.Determine the range of f.

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.

Let f(x)={(4x-5,xge2),(1-x,x 3):} be two functions from R to R. Find (gof)(1)

Let A = {1,2,3} . For x,y in A , Let xRy If and only if x gt y . Write down R as a subset of AxxA .