Rule of Conjunction
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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.
- If we can conclude both $\phi$ and $\psi$, we may infer the compound statement $\phi \land \psi$.
The Rule of Conjunction can be symbolised in sequent form as follows:
|\(\ds p\)||\(\)||\(\ds \)|
|\(\ds q\)||\(\)||\(\ds \)|
|\(\ds \vdash \ \ \)||\(\ds p \land q\)||\(\)||\(\ds \)|
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.