# 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:

- $p, q \vdash p \land q$

## 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** - the
**rule of adjunction**.