Rule of Conjunction

Axiom
The rule of conjunction is one of the axioms of natural deduction.

If we can conclude both $p$ and $q$, we may infer the compound statement $p \land q$.

It can be written:
 * $\displaystyle {p \qquad q \over p \land q} \land_i$

Sequent Form
The rule of conjunction is symbolised by the sequent:

Tableau Form
In a tableau proof, the rule of conjunction can be invoked in the following manner:


 * Abbreviation: $\land \mathcal I$
 * Deduced from: The pooled assumptions of each of $p$ and $q$.
 * Depends on: Both of the lines containing $p$ and $q$.

Explanation
This means: if we can show that two statements are true, then we may build a compound statement expressing this fact, and be certain that this is also true.

Thus a conjunction is added to a sequent.

Also known as
This is sometimes known as:


 * the rule of and-introduction;
 * the rule of adjunction.

Also see

 * Rule of Simplification