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

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

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

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.

Prove that the operation * an Z defined by a*b = a|b| for all a,b in Z is closed under*.

Let Z be the set of all integers and R be the relation on Z defined as R={(a , b); a ,\ b\ in Z , and (a-b) is divisible by 5.} . Prove that R is an equivalence relation.

Let * be a binary operations on Z and is defined by , a * b = a + b + 1, a, bin Z . Find the identity element.

Let f: N->Z be a function defined as f(x)=x-1000. Show that f is an into function.

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