Easy -1.2 This is a straightforward question testing basic understanding of logical converses and counterexamples. Students only need to write the converse statement (mechanical reversal of implication) and provide a single counterexample (e.g., n=3 gives 2n=6 which is even, but n is odd, not the converse). Requires minimal problem-solving and is simpler than typical proof questions.
6 The converse of the statement ' \(\mathrm { P } \Rightarrow \mathrm { Q }\) ' is ' \(\mathrm { Q } \Rightarrow P\) '.
Write down the converse of the following statement.
$$\text { ' } n \text { is an odd integer } \Rightarrow 2 n \text { is an even integer.' }$$
Show that this converse is false.
'If \(2n\) is an even integer, then \(n\) is an odd integer'
1
or: \(2n\) an even integer \(\Rightarrow\) \(n\) an odd integer
Showing wrong e.g. 'if \(n\) is an even integer, \(2n\) is an even integer'
1
or counterexample e.g. \(n = 2\) and \(2n = 4\) seen [in either order]
[2]
## Question 6:
| Answer | Marks | Guidance |
|--------|-------|----------|
| 'If $2n$ is an even integer, then $n$ is an odd integer' | 1 | or: $2n$ an even integer $\Rightarrow$ $n$ an odd integer |
| Showing wrong e.g. 'if $n$ is an even integer, $2n$ is an even integer' | 1 | or counterexample e.g. $n = 2$ and $2n = 4$ seen [in either order] |
| **[2]** | | |
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6 The converse of the statement ' $\mathrm { P } \Rightarrow \mathrm { Q }$ ' is ' $\mathrm { Q } \Rightarrow P$ '.\\
Write down the converse of the following statement.
$$\text { ' } n \text { is an odd integer } \Rightarrow 2 n \text { is an even integer.' }$$
Show that this converse is false.
\hfill \mbox{\textit{OCR MEI C1 Q6 [2]}}