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

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 in Z,b in Z, a^2 =b^2} . Find : R.

Let R be the relation on Z defined by : R ={(a,b) :a in Z,b in Z, a^2 =b^2} . Find : domain of R.

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

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

Let R be the relation on Z defined by : R ={(a,b) :a in Z,b in Z, a^2 =b^2} . Find : range of R.

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

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 : (a, b) in R implies that (b, a) in R.