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Cm 1020 mathematics and programming

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Describe the following set using the listing method:A={x:x∈Zand0≤x3<100}[2]ii. Rewrite the following set using the set builder method:B={−1,1/2,−1/3,1/4,−1/5,1/6,···}[2](b) In a survey of 200 student, it was found that: 150 students took programming(P), 80 students took mathematics (M), 55 students took art (A), 60 studentstook mathematics and programming (M & P), 25 students took took artand mathematics (A & M), 40 students took art and programming (A & P),and 15 students took art, mathematics and programming (A & M & P).i. Draw a Venn diagram to display this information.ii. Use Venn diagram to the find the number of students that took1. programming only2. two modules only3. mathematics and programming but not art[6](c) LetAandBbe two subsets of the universal setU. Prove or disprove thatP(A∪B) =P(A)∪P(B).[4](d) LetAandBbe two subset of a universal setU. Show that:A⊆B⇔A∪B=U

Cm 1020 mathematics and programming

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