Rule of Conjunction

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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.


Also see