Let f be the subset of `Z xx Z` defined by `f={(ab,a+b) : a,b in Z}`. Is f a function from Z to Z? Justify your answer.

Let A={1,2,3,4}, B={1,5,9,11,15,16} and f={(1,5),(2,9),(3,1),(4,5),(2,11)} Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B. Justify your answer in each case.

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

Let f={(1,1),(2,3),(0,-1),(,-1,-3)} be a linear function from Z into Z. Find f(x).

Let x,y in Z and suppose that a relation R on Z is defined by x R y if and only if x le y then