note that
and
represent true and false, respectively
| number |
equivalence |
rule name |
| E1 |
|
|
| E2 |
|
|
| E3 |
|
|
| E4 |
|
|
| E5 |
|
|
| E6 |
|
|
| E7 |
|
|
| E8 |
|
|
| E9 |
|
|
| E10 |
|
|
| E11 |
|
|
| E12 |
|
|
| E13 |
|
|
| E14 |
|
distributivity |
| E15 |
|
distributivity |
| E16 |
|
de morgan |
| E17 |
|
de morgan |
| E18 |
|
|
| E19 |
|
|
| E20 |
|
|
| E21 |
|
|
| E22 |
|
|
| E23 |
|
|
| number |
implication |
rule name |
| I1 |
|
|
| I2 |
|
|
| I3 |
|
|
| I4 |
|
|
| I5 |
|
|
| I6 |
|
|
| I7 |
|
|
| I8 |
|
|
| I9 |
|
|
| I10 |
|
|
| I11 |
|
|
| I12 |
|
|
| I13 |
|
|
| I14 |
|
|
logical implication
| number |
implication |
| I'1 |
|
| I'2 |
|
| I'3 |
|
| I'4 |
|
| I'5 |
|
| I'6 |
|
| I'7 |
|
| I'8 |
|
| I'9 |
|
| I'10 |
|
| name |
rule of inference |
| Universal Instantiation |
where
is some arbitrary element of the universe |
| Universal Generalization |
where
holds for every element
of the universe |
| Existential Instantiation |
where
is some element of the universe of discourse. it is not arbitrary but must be one for which
is true |
| Existential Generalization |
where
is an element of the universe |