| Date | May 2015 | Marks available | 2 | Reference code | 15M.1.sl.TZ2.11 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Write down | Question number | 11 | Adapted from | N/A |
Question
\(p:x\) is a multiple of \(12\)
\(q:x\) is a multiple of \(6\).
Write down in words \(\neg p\).
Write down in symbolic form the compound statement
\(r:\) If \(x\) is a multiple of \(12\), then \(x\) is a multiple of \(6\).
Consider the compound statement
\(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple of \(12\).
Identify whether \(s:\) is the inverse, the converse or the contrapositive of \(r\).
Consider the compound statement
\(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple of \(12\).
Determine the validity of \(s\). Justify your decision.
Markscheme
\(x\) is not a multiple of \(12\) (A1) (C1)
\(p \Rightarrow q\) (A1)(A1)(C2)
Note: Award (A1) for \( \Rightarrow \), (A1) for \(p\) and \(q\) in the correct order.
Accept \(q \Leftarrow p\).
Converse (A1) (C1)
not valid (A1)
for example \(18\) is a multiple of \(6\) and not a multiple of \(12\) (R1) (C2)
Notes: Do not award (A1)(R0). Any multiple of 6 that is not a multiple of \(12\) can be accepted as a counterexample.
