AQA
Further AS Paper 2 Discrete
2019
June
— Question 4
2 marks
Exam Board
AQA
Module
Further AS Paper 2 Discrete (Further AS Paper 2 Discrete)
Year
2019
Session
June
Marks
2
Topic
Matchings and Allocation
4
State the definition of a bipartite graph.
4
A jazz quintet has five musical instruments: bassoon, clarinet, flute, oboe and violin. Jay, Kay, Lee, Mel and Nish are musicians and each plays a musical instrument in the jazz quintet.
Jay knows how to play the bassoon and the clarinet.
Kay knows how to play the bassoon, the oboe and the violin.
Lee knows how to play the clarinet and the flute.
Mel knows how to play the clarinet, the oboe and the violin.
Nish knows how to play the flute, the oboe and the violin.
4
Draw a graph to show which musicians know how to play which instruments.
4
(ii) Nish arrives late to a jazz quintet rehearsal.
Each of the other four musicians is already playing an instrument:
\begin{displayquote}
Jay is playing the clarinet
Kay is playing the oboe
Lee is playing the flute
Mel is playing the violin.
\end{displayquote}
Explain how the graph in part (b)(i) shows that there is no instrument available that Nish knows how to play.
4
(iii) When Nish arrives the rehearsal stops. When they restart the rehearsal, Nish is playing the flute.
Draw all possible subgraphs of the graph in part (b)(i) that show how Jay, Kay, Lee and Mel can each be assigned a unique musical instrument they know how to play. [0pt]
[2 marks]