Answer
(a)
The provided compound statement can be written in simple statements as\[p,q,r\].
Here, \[p,\text{ }q,\text{ }r\]represents three simple statements:
\[p:\]I fail the course.
\[q:\]I rely on a used book with highlights by an idiot.
\[r:\] I buy a used book.
Therefore, the compound statement can be written in the symbolic form as:
\[\left( p\leftrightarrow q \right)\vee \sim r\]
(b)
The truth table is as follows:
(c)
So, from the truth table, it can be stated that when the component of provided compound statement\[\left( p\leftrightarrow q \right)\vee \sim r\], has false truth value, then only resultant statement is false.
Therefore, the statement is true when p, q, and r are all true.
