| Exam Board | OCR MEI |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2012 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Logical statements and converses |
| Difficulty | Easy -1.8 This is a very accessible question testing basic logical reasoning and truth tables. Part (a) is everyday logic requiring no mathematical formalism, part (b) is a straightforward truth table application with explicit guidance, and part (c) is a simple modus tollens argument. All parts are significantly easier than typical A-level proof questions which require constructing original mathematical arguments. |
| Spec | 1.01b Logical connectives: congruence, if-then, if and only if |
I appreciate you providing this task, but the content you've provided appears to be just a single row of numbers without any actual mark scheme content, marking annotations (M1, A1, B1, etc), or guidance notes to clean up.
Could you please provide the complete mark scheme content that needs formatting? It should include elements like:
- Mathematical content with unicode symbols to convert
- Marking annotations (M1, A1, B1, DM1, etc.)
- Guidance notes or criteria
- Question structure
Once you provide the full mark scheme, I'll be happy to clean it up and convert it to LaTeX notation as requested.1
\begin{enumerate}[label=(\alph*)]
\item When marking coursework, a teacher has to complete a form which includes the following:\\
□\\
In your opinion is this the original work of the pupil? (tick as appropriate)\\
I have no reason to believe that it is not □\\
I cannot confirm that it is □
\begin{enumerate}[label=(\roman*)]
\item The teacher suspects that a pupil has copied work from the internet. For each box, state whether the teacher should tick the box or not.
\item The teacher has no suspicions about the work of another pupil, and has no information about how the work was produced. Which boxes should she tick?
\item Explain why the teacher must always tick at least one box.
\end{enumerate}\item Angus, the ski instructor, says that the class will have to have lunch in Italy tomorrow if it is foggy or if the top ski lift is not working. On the next morning Chloe, one of Angus's students, says that it is not foggy, so they can have lunch in Switzerland.
Produce a line of a truth table which shows that Chloe's deduction is incorrect. You may produce a complete truth table if you wish, but you must indicate a row which shows that Chloe's deduction is incorrect.
\item You are given that the following two statements are true.
$$\begin{aligned}
& ( \mathrm { X } \vee \sim \mathrm { Y } ) \Rightarrow \mathrm { Z } \\
& \sim \mathrm { Z }
\end{aligned}$$
Use Boolean algebra to show that Y is true.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI D2 2012 Q1 [16]}}