Write down in words $(q \vee \neg r) \Rightarrow p$.

Complete the truth table.

State whether the statement $\neg p \Rightarrow \neg (q \vee \neg r)$ is the inverse, the converse or the contrapositive of the statement in part (a).

if the car is less than 2 years old or the car has not been driven more than $20\,000{\text{ km}}$, then the car is under warranty     (A1)(A1)(A1)     (C3)

Note:     Award (A1) for if …, then …, (A1) for “or”, (A1) for correct statements in correct order. Accept “If the car has not been driven more than $20\,000{\text{ km}}$ or the car is less than 2 years old, then the car is under warranty”. Accept logical equivalent wording for each proposition, eg “less than $20\,000{\text{ km}}$”.

[3 marks]

     (A1)(A1)(ft)     (C2)

Note:     Award (A1) for $q \vee \neg r$ column correct and (A1)(ft) for $(q \vee \neg r) \Rightarrow p$ column correct. Follow through from their $q \vee \neg r$ column.

[2 marks]

contrapositive     (A1)     (C1)

[1 mark]