SAMPLE EXAM I

  • Problem 1) Make a truth table for p; q; p or q; (not p) and use it to verify "{(p or q) and (not p)} implies q"
  • Problem 2) Find Union and Intersection of the sets B_n = (1 , 2 + 1/n) where n ranges over all natural numbers.
  • Problem 3) Let f be a function from A to B. Let C be a subset of A. Prove if f is injective, then f^{-1}(f(C))=C; that is, the pre-image by f of f(C) is C.
  • Problem 4) Let S and T be two subsets. Prove if S\T and T\S are equinumerous then S and T are equinumerous.
  • Problem 5) State the converse and contrapositive of the following statement: "The square of an odd integer has remainder 1 under division by 8".

    SAMPLE EXAM II

    Rough gradelines through two exams: