Summary
Negation(NOT)
| T | T |
| F | T |
Conjunction(AND)
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Disjunction(OR)
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Laws of boolean algebra
Concept
Order of operations ->
Tautology
Contradiction
Application
Logical equivalance
- solve via truth table
- LHS and RHS have the same truth values for all choices of truth values of the variables
only one row of the truth table is required to disprove logical equivalance
| LHS: | RHS: | |||||
|---|---|---|---|---|---|---|
| T | T | T | T | T | T | T |
| T | T | F | T | F | F | T |
| Solving via boolean algebra |
Exclusive-OR(XOR)
true iff only one of the variables are true
| LHS: | RHS: | |||||
|---|---|---|---|---|---|---|
| T | T | F | T | T | F | F |
| T | F | T | T | F | T | T |
| F | T | T | T | F | T | T |
| F | F | F | F | F | T | F |