91Ó°ÊÓ

To clarify the statement, let's group it using brackets to make the implications clearer: \((q \rightarrow p) \leftrightarrow (p \vee (q \rightarrow \sim p))\)

Now, let's construct the truth table. To do this, we need to note down all the possible combinations of 'true' (T) and 'false' (F) for statements p and q. Then, we calculate the truth values of \(q \rightarrow p\) and \(q \rightarrow \sim p\) respectively. We then find the truth value for \(p \vee (q \rightarrow \sim p)\) and finally for the entire statement.

The completed truth table would look like this: | p | q | \(q \rightarrow p\) | \(\sim p\) | \(q \rightarrow \sim p\) | \(p \vee (q \rightarrow \sim p)\) | \((q \rightarrow p) \leftrightarrow (p \vee (q \rightarrow \sim p))\) ||---|---|------------------|-------|---------------------|------------------------------|---------------------------------------------------------|| T | T | T | F | F | T | T || T | F | T | F | T | T | T || F | T | F | T | T | T | F || F | F | T | T | T | T | T |