OCR
Further Discrete AS
2022
June
— Question 7
1 marks
Exam Board
OCR
Module
Further Discrete AS (Further Discrete AS)
Year
2022
Session
June
Marks
1
Topic
Combinations & Selection
7
List the 15 partitions of the set \(\{ \mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } \}\) in which A and E are in the same subset.
By considering the number of subsets in each of the partitions in part (a), or otherwise, explain why there are 8 partitions of the set \(\{ \mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } \}\) into two subsets with A and E in different subsets.
Ali says that each of the 15 partitions from part (a) can be used to give two partitions in which A and E are in different subsets by moving E into a subset on its own or by moving E into another subset. [0pt]
By considering the partition from part (a) into just one subset, show that Ali is wrong. [1]
By considering a partition from part (a) into more than two subsets, show that Ali is wrong.