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 = R - {3} and B =R -{1}. Consider the function f : A to B defined by f (x) = ((x -2)/(x -3)). Is f one-one and onto ? Justify your answer.

Let R be the relation on Z defined by R= {(a,b): a, b in Z, a-b is an integer}. Find the domain and range of R.

Let f : R rarr R be defined by f(x) = cos (5x+2). Is f invertible? 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.

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

On Z defined * by a ** b = a -b show that * is a binary operation of Z.

Which of the following functions from Z into Z is a bijection?

Show that the function f : Z to Z defined by f(x) = x^(3), AA x in Z is injective but not surjective.

Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=b , then f is