Short But Important Words | ||||
---|---|---|---|---|

Conjunction | Alternation | Negation | Conditional | Biconditional |

Quantification (how many such and such are we discussing?) | ||||

Universal Quantification: for every x, for any y, for all z, given any x for whatever y, given an arbitrary x, unquantified ("free") variables |
Existential Quantification: for some x, for at least one y, there is a z |
| ||

Rules of Equality | ||||

For all a, a=a (reflexive). If a=b, then b=a
(symmetric). If a=b and b=c, then a=c (transitive). Generally
speaking, equal objects may be substituted for one another in
various expressions. For example, if a=b, then cos(a)=cos(b) and a
^{3}=b^{3}. |

- Conjunction Distributes across Alternation.
- Alternation Distributes across Conjunction.
- Negation of a Conjunction.
- Negation of an Alternation
- Negation of a Condtional
- Non-Contradiction, Excluded Middle, and Self Implication.
- Contrapositives.