Easy -1.2 This is a straightforward question requiring only a single counter-example with no calculation or proof construction. Students need only recall that irrational numbers can sum to rational (e.g., √2 + (-√2) = 0 or √2 + (1-√2) = 1), making this easier than average.
For example, let \(x = \pi + 4\), \(y = -\pi + 4\)
M1
Choosing \(x\) and \(y\) such that both are irrational. May not see \(x=, y=\)
\(x + y = (\pi + 4) + (-\pi + 4) = 8\) which is rational (and hence the statement is disproved)
A1
\(x\) and \(y\) chosen so that \(x + y\) is rational. Must comment that answer is rational (oe) and therefore the statement is disproved.
[2]
## Question 3:
| Answer | Marks | Guidance |
|--------|-------|----------|
| For example, let $x = \pi + 4$, $y = -\pi + 4$ | M1 | Choosing $x$ and $y$ such that **both** are irrational. May not see $x=, y=$ |
| $x + y = (\pi + 4) + (-\pi + 4) = 8$ which is rational (and hence the statement is disproved) | A1 | $x$ and $y$ chosen so that $x + y$ is rational. Must comment that answer is rational (oe) and therefore the statement is disproved. |
| **[2]** | | |
---
3 Give a counter example to disprove the following statement.\\
If $x$ and $y$ are both irrational then $x + y$ is irrational.
\hfill \mbox{\textit{OCR PURE Q3 [2]}}