Answer
\[p\vee \left( q\to \sim r \right)\]
Work Step by Step
The given compound statement can be written in simple statements as \[p,\text{ }q,\text{ and }r\]. Here, \[p,\text{ }q,\text{ and }r\] represents three simple statements.
\[p\]: The lines go down.
\[q\] : The transformer blows.
\[r\] : We have power.
Use the representation to re-write the statement as:
p, or if q then not r.
‘If-then’ is represented by the symbol ‘\[\to \]’, ‘Or’ is represented by the symbol ‘\[\vee \]’, and ‘Not’ is represented by the symbol ‘\[\sim \]’.
Use the symbols to write the compound statement in symbolic form as:
\[p\vee \left( q\to \sim r \right)\]