- Equivalences / simplifications (look at MATH 161 coursebook too)
- De Morgan’s laws
- Conjunctive and disjunctive normal forms
- Conjuction elimination
If A \land B is true, then both A and B are also true.
- Conjuction introduction
If both A and B are true, then A \land B is also true.
- Implication elimination
If both A and A \limplies B are true, then B is also true.
- Implication introduction
If both A \limplies B and B \limplies C are true, then then A \limplies C is also true.
- Disjuction introduction
If A is true, then both A \lor B and B \lor A are true for any B.
- Disjuction elimination
If A \lor B is true, then \lnot A implies B is true and \lnot B implies A is true.
- Negation introduction
If A \limplies (B \land (\lnot B)), then \lnot A.
- Double negation
\lnot(\lnot A) is equivalent to A.