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write a proof sequence for the following assertion. justify each step. (p ∨ q) ∨ (p ∨ r) ⇒ ¬r → (p ∨ q)

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

https://brainly.com/question/24191420

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