Answer
The truth table is as follows:
And the given compound statement is false when is false and is true
Work Step by Step
The given compound statement can be written in simple statements as\[p,q\].
Here, \[p,q\]represent two simple statements.
\[\begin{align}
& p:\ \text{Loving}\ \text{a}\ \text{person}\text{.} \\
& q:\ \text{Marrying}\ \text{a}\ \text{person}\text{.} \\
\end{align}\]
The given statement can be written in the symbolic form as
\[\left( q\to p \right)\wedge \left( \sim p\to \sim q \right)\].
The truth table for \[\left( q\to p \right)\wedge \left( \sim p\to \sim q \right)\] can be deduced by first finding the negation of \[p,q\]as\[\sim p,\sim q\].Now find the following conditional\[\left( q\to p \right)\], it is true when the former statement is true and the latter is false. In rest, all other cases it is true. Similarly, find\[\left( \sim p\to \sim q \right)\].Now, as these statements\[\left( q\to p \right)\], \[\left( \sim p\to \sim q \right)\] are joined by conjunction \[\wedge \] which is true only when both simple statements are true.
To construct the truth table draw the table having \[5\ \text{rows}\ \text{and}\ 7\ \text{columns}\] in which the elements of the first row are\[p,q,\sim p,\sim q,\left( q\to p \right),\left( \sim p\to \sim q \right),\left( q\to p \right)\wedge \left( \sim p\to \sim q \right)\].
