1. Let H be a normal subgroup of a group G. Define j: G ® G/H by: (a) j(ab) = j(a)j(b) (b) j(a) = Ha (c) j(Ha) = a (d) j(ab) = Hab (e) j(ab) = HaHb

2. Let H be a normal subgroup of a group G. Define j: G ® G/H by j(a) = Ha. Is j a homomorphism? (a) Yes (b) No

3. Let H be a normal subgroup of a group G. Define j: G ® G/H by j(a) = Ha. Is j one-to-one? (a) Yes (b) No

4. Let H be a normal subgroup of a group G. Define j: G ® G/H by j(a) = Ha. Is j onto? (a) Yes (b) No

5. Let G be any group. Define j: G ® G  Z 2 by: (a) j(ab) = j(a)j(b) (b) j(g) = (g 1, g 2 ) (c) j(g 1, g 2 ) = g 1 (d) j(a) = (a, 0) (e) j(g) = (g, 1)

6. Let G be any group. Define j: G ® G  Z 2 by j(a) = (a, 0). Is j a homomorphism? (a)Yes (b) No

7. Let G be any group. Define j: G ® G  Z 2 by j(a) = (a, 0). Is j one-to-one? (a)Yes (b) No

8. Let G be any group. Define j: G ® G  Z 2 by j(a) = (a, 0). Is j onto? (a)Yes (b) No

9. Define j: S n ® Z 2 by: (a) j(ab) = j(a)j(b) (b) j(a) = Ha (c) j(g 1, g 2 ) = g 1 g 2 (d) j(f) = 0 if f is even, 1 if f is odd (e) j(f) = 0 if f is odd, 1 if f is even

10. Define j: S n ® Z 2 by j(f) = 0 if f is even, 1 if f is odd Is j a homomorphism? Yes No

11. Define j: S n ® Z 2 by j(f) = 0 if f is even, 1 if f is odd Is j one-to-one? Yes No

12. Define j: S n ® Z 2 by j(f) = 0 if f is even, 1 if f is odd Is j onto? Yes No