Chapter 4

Page 66

  1. Associativity of AND and OR is shown in Tables 4-3 and 4-4 in the book.
  2. AND and OR identity values

    x x ∧ 1
    0 0
    1 1
    x x ∨ 0
    0 0
    1 1
  3. AND and OR commutativity

    x y x∧y y∧x
    0 0 0 0
    0 1 0 0
    } 1 0 0 0
    1 1 1 1
    x y x∨y y∨x
    0 0 0 0
    0 1 1 1
    } 1 0 1 1
    1 1 1 1
  4. AND distributive over OR

    x y z (y∨z) (x∧y) (x∧z) (x∧(y∨z) (x∧y)∨(x∧z)
    0 0 0 0 0 0 0 0
    0 0 1 1 0 0 0 0
    0 1 0 1 0 0 0 0
    0 1 1 1 0 0 0 0
    1 0 0 0 0 0 0 0
    1 0 1 1 0 1 1 1
    1 1 0 1 1 0 1 1
    1 1 1 1 1 1 1 1
  5. AND annulment

    x x ∧ 0
    0 0
    1 0
  6. Involution of NOT

    x (¬x) ¬(¬x)
    0 1 0
    1 0 1
  7. OR distributive over AND is shown in Table 4-5 in book.

  8. OR annulment value

    x x ∨ 1
    0 1
    1 1
  9. AND and OR complements

    x ¬x x ∧ ¬x
    0 1 0
    1 0 0
    x ¬x x ∨ ¬x
    0 1 1
    1 0 1
  10. AND and OR idempotency

    x x∧x
    0 0
    1 1
    x x∨x
    0 0
    1 1
  11. De Morgan’s law

    x y (x∧y) ¬(x∧y) ¬x ¬y ¬x ∨ ¬y
    0 0 0 1 1 1 1
    0 1 0 1 1 0 1
    1 0 0 1 0 1 1
    1 1 1 0 0 0 0
    x y (x∨y) ¬(x∨y) ¬x ¬y ¬x ∧ ¬y
    0 0 0 1 1 1 1
    0 1 1 0 1 0 0
    1 0 1 0 0 1 0
    1 1 1 0 0 0 0

Page 87

  1. a
  2. b
  3. c
  4. d
  5. e
  6. f