Propositions can be simplified to make them simpler to understand.
- Idempotence: and .
- Excluded middle: and
- Identity: and .
- Strictness: and .
- Double negation
This is easily provable: construct truth tables with rows for and .
There is a convention of priority among connectives, together with the associativity of and , reduces the need for brackets. The list below is order from the highest priority to lowest: