Provide symbolic logic proofderivation PQRQvP P PvR therefor

Provide symbolic logic proof/derivation

~(P&Q)->(R->(QvP)), ~P, PvR, therefore: Q

Answer :

The premises are given by

~ ( P & Q ) ( R ( Q v P ) )

~ P

P v R

And the conclusion is Q

Now we prove that the conclusion Q is logically follows from the given premises

Proof :

1. ~ P Premise

2. P v R Premise

3. R ( 1 ) , ( 2 ) Disjunctive syllogism

4. ~ ( P & Q ) ( R ( Q v P ) ) Premise

5. ~ [ ~ ( P & Q ) ] V ( ~ R V ( Q v P ) ) ( 4 ) rule of implication

6. ( P & Q ) V ( ~ R V ( Q v P ) ) ( 5 ) rule of double negation

7 . ~ R V ( Q v P ) ( 6 ) ( P & Q ) F since P is False as ~ P is premise it is true

8 . Q v P ( 3 ) , ( 7 ) , Disjuctive syllogism

9. Q ( 1 ) , ( 8 ) , Disjuctive syllogism

Thus the conclusion Q is logically follows from the given premises