Answer
Use letters to represent each simple statement in the argument.
p: I tell you I cheated.
q: I’m miserable.
Express the premises and conclusion symbolically as:
\[\frac{\begin{align}
& p\to q \\
& \sim p\to q \\
\end{align}}{\therefore q}\ \ \ \ \ \frac{\begin{align}
& \text{If I tell you I cheated, I }\!\!'\!\!\text{ m miserable}\text{.} \\
& \text{If I don }\!\!'\!\!\text{ t tell you I cheated, I }\!\!'\!\!\text{ m miserable}\text{.} \\
\end{align}}{\therefore \text{I }\!\!'\!\!\text{ m miserable}\text{.}}\]
Write a symbolic statement of the form - \[\left[ \left( \text{premise}\ \text{1} \right)\wedge \left( \text{premise}\ \text{2} \right) \right]\to \text{conclusion}\]
The symbolic statement is:
\[\left[ \left( p\to q \right)\wedge \left( \sim p\to q \right) \right]\to q\]
Construct a truth table for the statement\[\left[ \left( p\to q \right)\wedge \left( \sim p\to q \right) \right]\to q\] as shown below:
Work Step by Step
