Suppose f is a function from A to B where A and B are finite sets with |A| = |B|. Show that f is one to one if and only if it is onto. Solution . Let f : A ---> B be function. . Given |A = |B| . Suppose that f is one to one function. . i.e., f(x) = f(y) is B => x = y is A . with respect to the function of f, every element in B has apre-image in A. . f is onto. . Suppose that f is onto function. . Since each element is A has one and only one image in Band the number of elements in B . and the number of images of f are equal. . It follows that distinct elements in A have distinct images inB. . f is one to one. . Hence f is one to one if and only if it isonto. ..