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Sagot :
we proved that (p ∨ q) ∨ (p ∨ r) ⇒ ¬r → (p ∨ q)
given assertion is
(p v q) v ( p v r ) and we have to prove that
(p ∨ q) ∨ (p ∨ r) ⇒ ¬r → (p ∨ q)
we use addition property on Right hand side
(p v q) -> (p v q) v r
now we are using commutativity property
(p v q) -> r v (p v q)
(p v r) -> q v (p v r) addition
(p v r) -> (q v p) v r associativity
(p v r) -> (p v q) v r commutativity
(p v r) -> r v (p v q) commutativity
r v (p v q )
¬ ¬r v ( p v q) double negation
¬ r -> (p v q ) implication
Hence we proved that (p ∨ q) ∨ (p ∨ r) ⇒ ¬r → (p ∨ q)
learn more about of associativity here
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