ICS 6B
Fall 2013
Homework 4

Due: Wednesday, Oct 30

Covers Sections 2.1-2.4

Please indicate which section you are in at the top of your homework.

1. Define the following sets:
   • A = { x ∈ Z: x is an integer multiple of 3 }
   • B = { x ∈ Z: x is a perfect square }
   • C = {4, 5, 9, 10}
   • D = {2, 4, 11, 14}
   • E = {3, 6, 9}
   • F = {4, 9, 16}
   Circle the statements that are true:
   1. D ⊆ C
   2. E ∩ F = ∅
   3. E ∩ F ∩ D = ∅
   4. 27 ∈ A
   5. 27 ∈ B
   6. A ∩ E = E
   7. A ⊂ E
   8. 100 ∈ B
   9. C ∩ D ⊆ F
   10. 144 ∈ A ∩ B


2. What is the power set of {1}?


3. Let X = {1, {1}, {1, 2}, 2}.
   1. What is |X|?
   2. Circle the statements that are true:
      1. 2 ∈ X
      2. {2} ⊆ X
      3. {2} ∈ X
      4. 1 ∈ X
      5. {1, 2} ∈ X
      6. {1, 2} ⊆ X


4. What is the cardinality of P({1, 2, 3, 4, 5})?


5. Draw a Venn diagram illustrating the following sets:
   1. A ∪ B
   2. (A ∩ C) ∪ B
   3. (A ∪ B) ∪ (A ∩ C)
   4. (A ∩ B) ∪ (A ∩ C) ∪ (B ∩ C)
   5. A - (B ∩ C ∩ D)
   6. (A ∩ B) ∪ (C ∩ D)
   7. A ∩ (B-C)
   8. (A - B) ∪ (A - C) ∪ (B - C)


6. Give an example showing that subtraction is not associative: A - (B - C) ≠ (A - B) - C.


7. Define the following sets:
   • A = {milk, coffee}
   • B = {bacon, ham}
   • C = {eggs, pancakes}
   List the elements of AxBxC.


8. Indicate whether the following statements are true or false:
   1. R² ⊆ R³
   2. Z² ⊆ R²
   3. If A ⊆ B, then A² ⊆ B²
   4. Z³ ∩ Z² = ∅


9. Define the following sets:
   • A = {1, 2, 6}
   • B = {2, 3, 4}
   • C = {5}
   • D = {x ∈ Z: 1 ≤ x ≤ 6}
   Do A, B, and C form a partition of D? If not, which condition of a partition is not satisfied?


10. Define the following sets:
    • A = {x ∈ R: x < -2}
    • B = {x ∈ R: x > 2}
    • C = {x ∈ R: |x| < 2}
    Do A, B, and C form a partition of R? If not, which condition of a partition is not satisfied?