Answer
The given compound statement can be written in simple statements as \[p,\text{ and }q\]. Here, \[p,\text{ and }q\] represents three simple statements:
p: I am an intellectual.
q: I am pessimistic about America.
Use the representation to re-write the statement as:
If p, q but since not p, not q.
‘If-then’ is represented by the symbol ‘\[\to \]’, ‘But’ is represented by the symbol ‘\[\wedge \]’, and ‘Not’ is represented by the symbol ‘~’.
Use the symbols to write the compound statement in symbolic form as:
\[\left( \left( p\to q \right)\wedge \tilde{\ }p \right)\to \tilde{\ }q\]
