Mathematics 713 Assignment #1

    1.  Prove part (c) of Proposition 1.6 in McDonald and Weiss.

    2.  Let f:X->Y and A be a subset of X.  Prove or find a counter
        example to the claim

                  c           c
              f( A ) =  (f(A))   ,

        or in otherwords, that the image of A complement under f is
        the complement of the image of A under f.

    3.  [Extra Credit]  Let f:A->B and g:B->A be given by A=[0,1],
        B=[0,2], f(x)=1+x and g(y)=y/3.  Let h:A->B be the function
        defined on page 26 of McDonald and Weiss.  Compute h(0),
        h(1/4), h(1/2), h(3/4) and h(1).

    4.  Suppose A and B are sets and that there are onto functions
        f:A->B and g:B->A.  Prove or find a counter example to the
        claim

              A ~ B  ,

        or in otherwords, that the set A is set equivalent to B.

    5.  Work problem 1.39 in McDonald and Weiss.

    6.  Work problem 1.52 in McDonald and Weiss.