About This Unit
Boolean laws are rules used to simplify boolean expressions. Boolean expressions are written using boolean
symbols, which can be broken down
and represented visually with truth tables. In order to understand the purpose and function of boolean laws, we
must first understand
the basic symbols and their meanings as well as how they can be used to construct truth tables.
Boolean Symbols
NOTE: in the problem 6 solutions video, when I went over the distributive
property,
I should've pointed at the last and operator, not the operator between A and not B
Summary
| Symbol |
Meaning |
| p,q |
Statements |
| T |
True |
| F |
False |
| ∧ |
AND |
| ∨ |
OR |
| ¬ |
NOT |
| ≡ |
Equivalence |
Truth Tables
NOTE: in the problem 6 solutions video, when I went over the distributive
property,
I should've pointed at the last and operator, not the operator between A and not B
Summary
| p |
q |
p∧q |
| T |
T |
T |
| T |
F |
F |
| F |
T |
F |
| F |
F |
F |
| p |
q |
p∨q |
| T |
T |
T |
| T |
F |
T |
| F |
T |
T |
| F |
F |
F |
Boolean Laws
Practice
NOTE: in the problem 6 solutions video, when I went over the distributive property,
I should've pointed at the last and operator, not the operator between A and not B
Summary
Commutative: p ∨ q ≡ q ∨ p; p ∧ q ≡ q ∧ p
Associative: (p ∨ q) ∨ r ≡ p ∨ (q ∨ r ); (p ∧ q) ∧ r ≡ p ∧ (q ∧ r )
Distributive: p ∨ (q ∧ r ) ≡ (p ∨ q) ∧ (p ∨ r ); p ∧ (q ∨ r ) ≡ (p ∧ q) ∨ (p ∧ r )
Identity: p ∧ T ≡ p; p ∨ F ≡ p
Complement: p ∧ ¬p ≡ F ; p ∨ ¬p ≡ T
Annihilator: p ∧ F ≡ F ; p ∨ T ≡ T
Idempotence: p ∧ p ≡ p; p ∨ p ≡ p
Absorption: p ∧ (p ∨ q) ≡ p; p ∨ (p ∧ q) ≡ p
Double negation: ¬(¬p) ≡ p
De Morgan’s: ¬(p ∧ q) ≡ ¬p ∨ ¬q; ¬(p ∨ q) ≡ ¬p ∧ ¬q