Rule of Conjunction

Sequent

The rule of conjunction is a valid argument in types of logic dealing with conjunctions $\land$.

This includes propositional logic and predicate logic, and in particular natural deduction.

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
• the rule of adjunction.

Also see

• Definition:Conjunction

• Rule of Simplification