Answer
(a)
The given compound statement can be written in simple statements \[p,q,r\] as shown below,
\[\begin{align}
& p\text{ : You cut and paste from the internet}\text{. } \\
& q\text{: }\ \text{You cite the source}\text{. } \\
& r\text{: }\ \text{You will be charged with plagiarism}\text{.} \\
\end{align}\]
Use the representation to re-write the provided statement as,
If p and not q, then r.
‘If-then’ is represented by the symbol ‘\[\to \]’, ‘Not or negation’ is represented by the symbol ‘\[\sim \]’, and ‘And’ is represented by the symbol ‘\[\wedge \]’.
Use the symbols to determine the symbolic form of the provided statement as,
\[\left( p\wedge \sim q \right)\to r\]
Hence, the symbolic form for the provided statement is, \[\left( p\wedge \sim q \right)\to r\].
(b)
The truth table is as follows:
c)
The truth table for \[\left( p\wedge \sim q \right)\to r\] is as follows:
It can be seen from the truth table that the statement \[\left( p\wedge \sim q \right)\to r\]is false when the statement \[p\wedge \sim q\] is true and the statement \[r\] is false.
Hence, the provided statement is false when \[p\wedge \sim q\text{ is true and r is false}\].
