Answer
(a)
The provided compound statement can be written in simple statements as\[p,\ q,\ r\].
Here, \[p,\ q,\ \text{and}\ r\]represent three simple statements.
\[p:\] You will be comfortable in your room.
\[q:\] You are honest with the roommate.
\[r:\] You will enjoy the college experience.
Therefore, the provided compound statements can be written in the symbolic form as
\[\left( p\leftrightarrow q \right)\vee \sim r\]
Hence, the provided 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.
