| Date | May 2010 | Marks available | 4 | Reference code | 10M.1.sl.TZ1.3 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Complete | Question number | 3 | Adapted from | N/A |
Question
Consider two propositions p and q.
Complete the truth table below.
Decide whether the compound proposition
\[\left( {{\text{ }}p \Rightarrow \neg q} \right) \Leftrightarrow \left( {\neg p \Rightarrow q} \right)\]
is a tautology. State the reason for your decision.
Markscheme
(A1)(A1)(ft)(A1)(A1)(ft) (C4)
Note: Award (A1) for each correct column (second column (ft) from first, fourth (ft) from third). Follow through from second column to fourth column for a consistent mistake in implication.
[4 marks]
Since second and fourth columns are not identical (R1)(ft)
\( \Rightarrow \) Not a tautology (A1)(ft) (C2)
Note: (R0)(A1) may not be awarded.
[2 marks]
Examiners report
The truth table was well done by the majority of candidates but significantly fewer could give the correct reason for whether the compound proposition was a tautology, so many lost 2 marks in this part of the question.
The truth table was well done by the majority of candidates but significantly fewer could give the correct reason for whether the compound proposition was a tautology, so many lost 2 marks in this part of the question.
