Conjunction Introduction

If two conjuncts have each been independently derived then they can be conjoined. Also known more simply as Conjunction

Strategies for constructing proofs in propositional logic
- Assume that we want to show that an argument is valid. Then our ultimate goal is to derive the conclusion from the premises we are given. We first ask ourselves: which propositions if we could derive them, would allow us to easily derive the conclusion? (For example, these propositions might be two simple propositions that when combined with Conjunction Introduction give us the conclusion.) Deriving these propositions then becomes the new intermediate goal.
- Now we need to get from \(L\) to \(L \lor A\). This is really straightforward because by using Disjunction Introduction) we can get from any sentence to a disjunction. Finally, having assembled all the constituent parts of the conjunction that is the conclusion, we can combine them with Conjunction Introduction as we had planned at the outset.
- The requirements here could easily mislead us. We see that the target proposition is a conjunction so we might think that the best strategy is to seek to derive each conjunct and then combine them via Conjunction Introduction).
Formal proofs in propositional logic
- Conjunction Introduction