| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Logical statements and converses |
| Difficulty | Easy -1.8 This is a very basic logic question testing understanding of odd/even properties and simple implications. All parts require only direct substitution or elementary reasoning about parity, with no calculation or proof construction needed. This is significantly easier than typical A-level questions. |
| Spec | 1.01b Logical connectives: congruence, if-then, if and only if |
4 Given that $n$ is a positive integer, write down whether the following statements are always true (T), always false (F) or could be either true or false (E).\\
(i) $2 n + 1$ is an odd integer\\
(ii) $3 n + 1$ is an even integer\\
(iii) $n$ is odd $\Rightarrow n ^ { 2 }$ is odd\\
(iv) $n ^ { 2 }$ is odd $\Rightarrow n ^ { 3 }$ is even
\hfill \mbox{\textit{OCR MEI C1 2008 Q4 [3]}}