1-page 16, 1.1.7 c&e

2-page 17, 1.1.9

3-page 17, 1.1.12 b

4-Show that p⇒q⇔¬p∨q

5-page 20, 1,2.4

6-page 20, 1.2.6 b,e,f,k

7-page 25, 1.2.18 b,d,j

8-page 26, 1.2.19 c

9-page 31, 1.3.11 c,d,h

10-page 39, 1.4.13 c,e,f

1) 2.2.7. d / page 53

2) 2.5.4 / page 59

3) 2.5.8 / page 61

4) 2.5.9 / page 61

5) 3.1.13 / page 67

6) 3.2.3 / page 68

7) 3.2.9. d,g / page 70 <3) 3.4.9 d

4) 3.4.18 (prove by induction)

5) 3.5.22 (Hint: Consider cases n=1, n=2, n=3 seperately and try to generalize the pattern)

6) 3.11.14

7) 3.11.15

8) 3.11.18

9) Find all non-isomorphic partial orders on a set of size 4.

10) Write an example of a total order which is not a well-order.

1) 3.3.12

2) 3.3.14

3) 3.4.9 d

4) 3.4.18 (prove by induction)

5) 3.5.22 (Hint: Consider cases n=1, n=2, n=3 seperately and try to generalize the pattern)

6) 3.11.14

7) 3.11.15

8) 3.11.18

9) Find all non-isomorphic partial orders on a set of size 4.

10) Write an example of a total order which is not a well-order.

1) Show that ⊗ defined on Z in class is well defined.

2) Show that the relation (a,b)≡(c,d) defined by ad=bc on A=ℤ×(ℤ\{0}) is an equivalent relation.

3) Show that ⊕ defined on Q in class is well defined.

4) 3.6.7 /p.94

5) 3.6.10 /p.94

6) 3.6.11 /p.94

7) 3.6.14 /p.95

8) Show that the relation f:ℚ→ℤ such that f((p/q))=p does NOT define a function

9) Let f(x)=(1/(1-x)) and g(x)=1-x. Find all possible composite functions (i.e., fof,gof,fog,gog,fofof,gofog,...)

10) Let f:A→B and g:B→C are functions. Show that gof is a bijection if and only if both f and g are bijections.

1) 4.1.7 b & d

2) 4.1.11

3) 4.2.4

4) 4.2.7

5) 4.2.15.c

6) 4.3.13 a & b

7) 4.4.4.6

8) Show that P(IN) (Power set) is uncountable.

9) Show that if A⊆B and A is uncountable then B is also uncountable.

10) Show that if A⊆B and B is countable then A is also countable.

Homework 6