Answer
(a)
The provided compound statement can be written in simple statements as\[p,q,r\].
Here, \[p,q,r\]represents three simple statements:
\[p:\] You will take more than one class with lots of reading.
\[q:\] You will have free time.
\[r:\] You will be in the library until 1 a.m.
Therefore, the provided compound statement can be written in the symbolic form as:
\[p\to \left( \sim q\wedge r \right)\]
(b)
The truth table is as follows:
c)
So, from the truth table, it can be stated that when the truth value of \[p\to \left( \sim q\wedge r \right)\] is false,then the former statement is true and the latter statement is false. In rest, all other cases it is true.
Therefore, the statement is true when p, q, and \[r\] are all false.