| NOT | |
|---|---|
| p | p' |
| 1 | 0 |
| 0 | 1 |
Not: a unary operator, such that when p is true, not p is
false.
| AND | ||
|---|---|---|
| p | q | p · q |
| 1 | 1 | 1 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 0 |
Conjunction: p AND q is true only when both p and
q are true.
| OR | ||
|---|---|---|
| p | q | p + q |
| 1 | 1 | 1 |
| 1 | 0 | 1 |
| 0 | 1 | 1 |
| 0 | 0 | 0 |
Disjunction: p OR q is false only when both p and q
are false.
| XOR | ||
|---|---|---|
| p | q | p Å q |
| 1 | 1 | 0 |
| 1 | 0 | 1 |
| 0 | 1 | 1 |
| 0 | 0 | 0 |
Exclusive Or: p XOR q is true only when either p or q is true, but not when both are true.
| Conditional | ||
|---|---|---|
| p | q | p ® q |
| 1 | 1 | 1 |
| 1 | 0 | 0 |
| 0 | 1 | 1 |
| 0 | 0 | 1 |
by alternate
representation
Conditional: If p then q if false only when the hypothesis is
true and the conclusion is false. Note that when the hypothesis is false the
conditional is vacuously true.
Order of precedence: