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Math · Advanced Math
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1. (a) For a set A, what is meant by the cardinality of set A denoted IAl? What is the cardinality of the set: (xz-10x<5) where Z is the set of Integer numbers? [5 marks] (b) For two sets A 1,2,4,8.16) and B 1,2,3,5,8,13) i. Determine and state A U B, A- B, IA BI and |AI BI i Comment on reasons whyl AU BI may not be the same as Al BI and A - B | may not be the same as JA BI. ii. Use a Venn diagram to explain in what circumstances |AU B and IA - B would be equal to IA IBI and IAl - IBI respectively [8 marks] (c) 100 students were asked which desktop operating systems they had used in the previous year from MacOS, Windows and Linux. The results were collated: 20 had used only MacOS and Windows, 16 had used only Linux, 45 had used MacOS, 7 had used only MacOS and Linux, 17 had used MacOS, Linux and Windows, 46 had used Windows and 5 had used only Linux and Windows. Denoting the sets of students that had used a particular operating system as M, W and L for MacOS, Windows and Linux respectively Show the information on a Venn diagram and determine: i. What is the cardinality of each set: IMI. WI and ILI? ii What is the value of IMn wn LI? ii. How many students had used Linux Operating System? v How many students had not used any of the Operating Systems? v. How many students had used only the Windows Operating System? vi. How many students had used only the MacOperating System?[12 marks]
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