Proof: Rules of Inference
Using Disjunction and Conjunction

The first three rules involve basic operations with disjunction and conjunction:

Simplification (Simp)
Conjunction (Conj)
Addition (Add)
pq
pq
p
q
p
q
___
or
___
___
___
___
p
q
pq
p v q
p v q

Simplification is often useful when we have a conjunction and can see that one conjunct is not relevant to the conclusion. Conjunction allows us to put together two statements into a single conjunctive statement. Addition allows us to introduce a new statement by adding it, in the form of a disjunction, to a statement we already have.

Each inference is easily proven valid by truth tables.


Disjunction and conjunction |
Hypothetical and disjunctive syllogisms | Dilemmas
Constructing a Proof

Proof

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