Why $( → ) → $ and $( ∧ ) → $ not equivalent Question: For this logical expression without truth table please: $( → ) → $ and $( ∧ ) → $ are not equivalent based on truth table below:

Problem: Answer based on truth table is NO. But how to find out that they are not using logical equivalences please?
 A: Using basic equivalences you can only demonstrate further equivalences … you can’t demonstrate non-equivalence using equivalences… or at least not using equivalences alone. Something you could do is using equivalences to transform a statement into some kind of ‘canonical’ form, where each statement has exactly one canonical form, where any two statements that ate equivalent have the same canonical form, and where two statements that are not equivalent will have different canonical forms.
We could treat, for example, $(p \land q \land r) \lor (p \land \neg q \land r) \lor (p \land \neg q \land \neg r) \lor (\neg p \land q \land r) \lor (\neg p \land q \land \neg r) \lor (\neg p \land \neg q \land r) \lor (\neg p \land \neg q \land\neg r)$ as a canonical form of $(p \land q) \to r$ … avoiding having to give an exact definition, I think the nature of this statement will give you the idea of what makes this ‘canonical’ … it basically picks out the rows of a systematically constructed truh-table where the statement is true
