Logic Question the rule of replacement For each of the follo

Logic Question (the rule of replacement)

*For each of the following, adding just two statements to the premises will produce a formal proof of validity. Construct a formal proof of validity for each of the following argument.

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(D . ~E) > F

~(E v F)

Therefore ~D

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Solution

Answer :

1. (D . ~E) > F   premise

2. ~(E v F)            premise

3. ~E . ~ F           ( 2 ) , Demorgan law

4. ~ E                ( 3 ) Rule of conjuction

5. ~ F                   ( 3 ) Rule of conjuction

6. ~ (D . ~E)      ( 1 ) , ( 4 ), Modus Tollen\'s rule

7 . ~ D v ~(~E)                 ( 6 ) , Demorgan law

8. ~ D v E                         ( 7 ) , Law of double negation

9. ~ D                               ( 4 ),( 8 ) , Disjunctive Syllogism

Thus ~ D is logically follows from the given premises and the given argument is valid