COMP 280 Assignment 6

The following problems total to 100 points.

  1. (12 points — 3 points each part) Rosen 6th ed. 2.3 #16a-d

    Give an example of a function from ℕ to ℕ that is

    1. one-to-one but not onto.
    2. onto but not one-to-one.
    3. both onto and one-to-one (but different from the identity function).
    4. neither one-to-one nor onto.
  2. (12 points — 3 points each part)

    Give an example of a function from ℕ to {true, false} that is

    1. one-to-one but not onto.
    2. onto but not one-to-one.
    3. both onto and one-to-one.
    4. neither one-to-one nor onto.

    If no such function exists, explain why.

  3. (8 points) Rosen 6th ed. 2.3 #30

    If f and fg are one-to-one, does it follow that g is one-to-one? Justify your answer.

  4. (5 points) Rosen 6th ed. 2.3 #36b

    Let f be a function from the set A to the set B. Let S and T be subsets of A. Show that f(ST) ⊆ f(S)∩f(T).

  5. (5 points) Rosen 6th ed. 2.3 #40a

    Let f be a function from A to B. Let S and T be subsets of B. Show that f-1(ST) = f-1(S)∪f-1(T).

  6. (5 points)