# Rule of Conjunction

## Sequent

The rule of conjunction is a valid deduction sequent in propositional logic.

### Proof Rule

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

### Sequent Form

The Rule of Conjunction can be symbolised in sequent form as follows:

 $\ds p$  $\ds$ $\ds q$  $\ds$ $\ds \vdash \ \$ $\ds p \land q$  $\ds$

## Explanation

The Rule of Conjunction can be expressed in natural language as:

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

The Rule of Conjunction can also be referred to as:

• the rule of and-introduction