Write a proof sequence for the following assertion Justify e

Write a proof sequence for the following assertion. Justify each step. p rightarrow q p r} rightarrow q r

Solution

The premises are p q and p r

and the conclusion is q r

proof :

1.   p q                premise

2.   ¬ p q              ( 1 ) law of implication : (p q) (¬ p q)

3.    p r                premise

4.     p                    ( 3 ) law of conjuction :( p r ) p

5.    r                     ( 3 ) law of conjuction :( p r ) r   

6.   q                     ( 1 ) and ( 4 ) modus pones rule: p (p q) q

7.    q r           ( 5 ) and ( 7 ) law of conjuction:

Hence, q r is logically follows from the given premises