Write in words the compound statement \(\neg p \wedge q\) .

Write the following statement in symbolic form.

“Either Carlos is playing the guitar or he is studying for his IB exams but not both.”

Write the converse of the following statement in symbolic form.

“If Carlos is playing the guitar then he is not studying for his IB exams.”

Carlos is not playing the guitar and he is studying for his IB exams.     (A1)(A1)     (C2)

Note: Award (A1) for “and”, (A1) for correct statements.

[2 marks]

\(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q\)     (A1)     (C1)

[1 mark]

\(\neg q \Rightarrow p\)     (A1)(A1)(A1)     (C3)

Notes: Award (A1) for implication, (A1) for the \(\neg q\), (A1) for both \(\neg q\) and \(p\) in the correct order. If correct converse seen in words only award (A1)(A1)(A0). Accept \(p \Leftarrow \neg q\). Accept \( - q\) for \(\neg q\).

[3 marks]

In part (a) occasionally ‘if…then…’ was not seen but generally this was well done.

Part (b) was also well done despite the dearth of previous testing of the exclusive or statement.

Finding the converse of a statement in part (c) proved to be difficult for a significant number of candidates and incorrect answers of the form \(q \Rightarrow \neg p \) were more frequently seen than the correct answer. Such incorrect answers lost two marks.