The following problems total to 100 points.
(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
(12 points — 3 points each part)
Give an example of a function from ℕ to {true, false} that is
If no such function exists, explain why.
(8 points) Rosen 6th ed. 2.3 #30
If f and f∘g are one-to-one, does it follow that g is one-to-one? Justify your answer.
(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(S∩T) ⊆ f(S)∩f(T).
(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(S∪T) = f-1(S)∪f-1(T).
(5 points)