Set 6.1: 3, 7, 13, 18, 33, 34
Logic Symbols: ≥ ≤ ≠ ¬ ∧ ∨ ⊕ ≡ → ↔ ∃ ∀ Set Symbols: ∈ ∉ ⊆ ⊂ ⊇ ⊃ ∅ ∪ ∩ ×
3. Let sets R, S, and T be defined as follows:
R = {x ∈ Z | x is divisible by 2}
S = {y ∈ Z | y is divisible by 3}
T = {z ∈ Z | z is divisible by 6}
a. Is R ⊆ T? Explain.
b. Is T ⊆ R? Explain.
c. Is T ⊆ S? Explain.
7. Let A = {x ∈ Z | x = 6a + 4 for some integer a}
B = {y ∈ Z | y = 18b - 2 for some integer b}
C = {z ∈ Z | z = 18c + 16 for some integer a}
Prove or disprove each of the following statements:
a. A ⊆ B
b. B ⊆ A
c. B = C
13. Indicate which of the following relationships are true and which are false:
a. Z^+ ⊆ Q b. R^- ⊆ Q
c. Q ⊆ z d. Z^- ∪ Z^+ = Z
e. Z^- ∩ Z^+ = ∅ f. Q ∩ R = Q
g. Q ∪ Z = Q h. Z^+ ∩ R = Z^+
i. Z ∪ Q = Z
18. a. Is the number 0 in ∅? Why?
b. Is ∅ = {∅}? Why?
c. Is ∅ ∈ {∅}? Why?
d. Is ∅ ∈ ∅? Why?
33. a. Find P(∅)
b. Find P(P(∅))
c. Find P(P(P(∅)))
34. Let A1 = {1, 2, 3}, A2 = {u, v}, and A3 = {m, n}. Find each of the following sets:
a. A1 x (A2 x A3) b. (A1 x A2) x A3 c. A1 x A2 x A3
