Chapter 4
Page 66
 Associativity of AND and OR is shown in Tables 43 and 44 in the book.

AND and OR identity values
x x ∧ 1 0
0
1
1
x x ∨ 0 0
0
1
1

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

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

AND annulment
x x ∧ 0 0
0
1
0

Involution of NOT
x (¬x) ¬(¬x) 0
1
0
1
0
1

OR distributive over AND is shown in Table 45 in book.

OR annulment value
x x ∨ 1 0
1
1
1

AND and OR complements
x ¬x x ∧ ¬x 0
1
0
1
0
0
x ¬x x ∨ ¬x 0
1
1
1
0
1

AND and OR idempotency
x x∧x 0
0
1
1
x x∨x 0
0
1
1

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
 a
 b
 c
 d
 e
 f