| Date | May 2011 | Marks available | 1 | Reference code | 11M.1.sl.TZ2.3 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Complete | Question number | 3 | Adapted from | N/A |
Question
In a particular school, students must choose at least one of three optional subjects: art, psychology or history.
Consider the following propositions
a: I choose art,
p: I choose psychology,
h: I choose history.
Write, in words, the compound proposition
\[\neg h \Rightarrow (p \vee a)\].
Complete the truth table for \(\neg a \Rightarrow p\) .
State whether \(\neg a \Rightarrow p\) is a tautology, a contradiction or neither. Justify your answer.
Markscheme
If I do not choose history then I choose either psychology or I choose art (A1)(A1)(A1) (C3)
Notes: Award (A1) for ‘if… (then)…’
Award (A1) for ‘not choose history.’
Award (A1) for ‘choose (either) psychology or art (or both).’
If the order of the statements is wrong award at most (A1)(A1)(A0).
[3 marks]
(A1) (C1)
[1 mark]
Neither, because not all the entries in the last column are the same. (A1)(ft)(R1) (C2)
Notes: Do not award (R0)(A1). Follow through from their answer to part (b). Reasoning must be consistent with their answer to part (b).
[2 marks]
Examiners report
Many correct answers were seen in part (a) with only a minority of candidates misinterpreting the symbol \( \vee \) as 'and'. Some candidates left out the word 'if' and consequently lost the first mark.
Part (b) was not done as well as expected indicating that some work needs to be done by centres on the truth table for the logic symbol \( \Rightarrow \) .
Many correct answers of 'neither' were seen in part (c) but the justification was sometimes lacking definitive reasoning. Without sufficient reasoning, the answer mark was not awarded.
