(Solved): b) Now consider whether 'implication' is associative. (i) Build a truth table that shows the value ...

b) Now consider whether 'implication' is associative. (i) Build a truth table that shows the values of \( p \rightarrow(q \rightarrow r) \) and of \( (p \rightarrow q) \rightarrow r \). (ii) Are \( p \rightarrow(q \rightarrow r) \) and \( (p \rightarrow q) \rightarrow r \) logically equivalent? (iii) Would it make sense to say that \( \rightarrow \) is associative? Note that we did not discuss \( \rightarrow \) in Lecture 1. It will be discussed in Lecture 2, but for this question, none of the context of that discussion is required, and it is sufficient to know that \( p \rightarrow q \) is described by the truth table on the right. Truth table for \( \rightarrow \)