4.2. Arguing from and for alternatives

4.2.0. Overview

Because a disjunction normally says less than its components while a conjunction says more, the two connectives play very different roles in entailment.

4.2.1. Proofs by cases
Since a disjunction says only what is said by both its disjuncts, it entails only what is entailed by both of them.

4.2.2. Proving disjunctions
Since a disjunction makes a relatively weak claim, it is easy to state a sound rule to plan for it, but a safe rule that will cover all cases where it holds is more complex.

4.2.3. Further examples
There are now many choices to be regarding the order in which rules are applied and some differences in the length of derivations can result.

4.2.4. The duality of conjunction and disjunction
Conjunction and disjunction are, in a certain formal sense, mirror images of one another.