1. Assume f: A  B and g: B  C are functions. Which are defined? (1) f  g (2) g  f(3) both(4) neither

2. Assume f: A  B and g: B  C are functions. What is the domain of g  f ? (1) A (2) B (3) C (4) f (5) g (6) B  A (7) B  C (8) f  g (9) g  f (10 or 0) A  B

3. Assume f: A  B and g: B  C are functions. What is the codomain of g  f ? (1) A (2) B (3) C (4) f (5) g (6) B  A (7) B  C (8) f  g (9) g  f (10 or 0) A  B

4. What is the next line of this proof? (1) Let a  A. (2) Let (x,y)  A. (3) Let a  g  f. (4) Let (x,y)  g  f. (5) Let a  Dom(g  f). (6) Let (x,y)  Dom(g  f).

5. What is the next line of this proof? (1) Then a  Dom(f).(2) Then (a, b)  Dom(f) (3) Then a  g  f.(4) Then (a,b)  g  f. (5) Then a  Dom(g  f).(6) Then (a,b)  Dom(g  f). (7) Then a  f.(8) Then (a,b)  f (9) Then (a,b)  A.(10) Then f(a) = b.