Exercise 1.53.

(a)A = {−3,−2,−1, 0, 1, 2, 3}(b)B = {0, 1, 2}(c)C = {1, 2, 3, 4}(d)D = {0, 1}(e)E = ∅

Exercise 1.7.

(a)A = {x+ 3 : x ∈ Z}(b)B = {5x : x ∈ Z}(c)C = {x3 : x ∈ N}

Exercise 1.9.

C = {5, 7, 8}

Exercise 1.12.

A = B = D = E

Exercise 1.14.

(a)P(A) = {∅, 1, 2, 1, 2}, |P(A)| = 4

(b)P(A) = {∅, 1, a, 1, a}, |P(A)| = 4

Date: February 15, 2015.

2

Exercise 1.20.

(a)False

(b)False

(c)False

(d)True

Exercise 1.21.B = {1, 4, 5}

Exercise 1.23.

A = {1, 2, 3, 4, 5, 6}B = {1, 2, 3, 7, 8, 9}

Exercise 1.24.

A = {1, 2, 3, 4, 5, 6}B = {1, 2, 3, 7, 8, 9}C = {4, 5, 6, 7, 8, 9}

Exercise 1.30.

(a)A = [−1, 3]B = [−∞,−1] ∪ [1,∞]

C = [−5, 1](b)A ∪B = [−∞,∞]

A ∩B = [−1] ∪ [1, 3]

B ∩ C = [−5,−1] ∪ [1]

B − C = [−∞,−5) ∪ (1,∞]

3

Exercise 1.36.

∪α∈S Sα = [0, 6]

∩α∈S Sα = [3]

Exercise 1.43.

∪r∈R+ Ar = (0,∞]

∩r∈R+ Ar = (0,∞]

Exercise 1.45.

∪n∈N An = (0, 2)

∩n∈N An = (0, 1)

Exercise 1.46. (a) Yes S1 it is a partition.(b) S2 is not a partition, since ∪S∈SS 6= A.(c) Yes S3 it is a partition.(d) S4 is not a partition, since ∅ ∈ S2.(e) S5 is not a partition, since {b,g} and {b,f} are disjoint.