Easy -1.2 This question tests basic understanding of logical converses and requires a simple counterexample. Students only need to write 'if 2n is even then n is odd' and provide any even value of n (like n=2) to disprove it. This is straightforward recall and application with minimal problem-solving, making it easier than average.
3 The converse of the statement ' \(P \Rightarrow Q\) ' is ' \(Q \Rightarrow P\) '.
Write down the converse of the following statement.
' \(n\) is an odd integer \(\Rightarrow 2 n\) is an even integer.'
Show that this converse is false.
Converse: '\(2n\) is an even integer \(\Rightarrow\) \(n\) is an odd integer'
B1
Correct converse stated
Counterexample: e.g. \(n = 2\), \(2n = 4\) is even but \(n\) is not odd
B1
Valid counterexample shown
## Question 3:
Converse: '$2n$ is an even integer $\Rightarrow$ $n$ is an odd integer' | B1 | Correct converse stated
Counterexample: e.g. $n = 2$, $2n = 4$ is even but $n$ is not odd | B1 | Valid counterexample shown
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3 The converse of the statement ' $P \Rightarrow Q$ ' is ' $Q \Rightarrow P$ '.\\
Write down the converse of the following statement.\\
' $n$ is an odd integer $\Rightarrow 2 n$ is an even integer.'\\
Show that this converse is false.
\hfill \mbox{\textit{OCR MEI C1 2007 Q3 [2]}}