Simplification
| Rules of inference |
|---|
| Propositional calculus |
| Modus ponens Modus tollens Modus ponendo tollens Conjunction introduction Simplification Disjunction introduction Disjunction elimination Disjunctive syllogism Hypothetical syllogism Constructive dilemma Destructive dilemma Biconditional introduction Biconditional elimination |
| Predicate calculus |
| Universal generalization Universal instantiation Existential generalization Existential instantiation |
In mathematical logic, simplification (equivalent to conjunction elimination) is a valid argument and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.
In formal language:
or
The argument has one premise, namely a conjunction, and one often uses simplification in longer arguments to derive one of the conjuncts.
An example in English:
- It's raining and it's pouring.
- Therefore it's raining.