just finished proving an argument without the use of truth tables and was wondering if my reasoning is sound.
The problem given was
Prove using a proof sequence that the argument is valid (hint: the last A’ has to be inferred). Justify each step with a comment.
$(A\rightarrow C)\land(C\rightarrow\neg B) \land B\rightarrow\neg A$
- A -> C given
- C -> B' given
- B given
- A -> B' hypothetical syllogism of 1 and 2
- (B')' -> A' contrapositie of 4
- B -> A' double negation of 5
- A' modus ponens from 6,3
This answer seems correct to me but I am new to solving these types of problems and any input would be appreciated.