Name: ______________________ ( ) Class: __________ Date: __________________ Fundamental Concepts & Set Theory  QUIZ Question 1: Suppose that: [13] π΄ = {1, 2, 3, 6, 7} , π΅ = {4, 7, 12, 2, 3} , πΆ = {1, 3, 2, 7, 8, 9} , π· = {7, 3, 1, 2, 6} π=β€ Fill in the symbols β, β, β, β, β, β for the following: a) π΄ _____ π· b) {4, 7, 12} _____ π΅ c) 6 _____ πΆ d) {1, 2, 3, 4, 5, 6, 7, 12} _____ π΅ e) 7 _____ π· f) β _____ πΆ g) π΄ _____ π h) π· _____ β i) π _____ β j) 30 _____ π k) π΅ _____ π· l) π _____ π΄ m) β _____ π Question 2: Please write down the cardinality of the following sets: [3] a) πΈ = {1, 4, 1, 2} π(πΈ) = ______ b) πΉ = {1, 2, 3, 5, 8} βͺ {6, 7, 9} π(πΉ) = ______ c) πΊ = {1, 2, 3, 6, 9} β© {7, 12, 5, 1, 6} π(πΊ) = ______ Question 3: The following questions are about setbuilder notation: [6] π a) Please write down this set into roster notation: π» = {π : π, π β β€, 0 β€ π β€ 2, β3 β€ π < 0} __________________________________________________________________________________ __________________________________________________________________________________ b) Please rewrite this set into setbuilder notation: πΎ = {Odd numbers} __________________________________________________________________________________ __________________________________________________________________________________ Question 4: Please answer the following Venn Diagram question: Question 5: The average thickness of ice in the North Pole has been decreasing due to global warming. a) In May 2000, the thickness is around 0.05% of the depth of the ocean in the North pole, which is 4000 metres in average. Find the thickness of ice in May 2000. [2] __________________________________________________________________________________ __________________________________________________________________________________ b) After 21 years, the thickness of ice is now 1.8 metres. Find the percentage change from May 2000 to May 2021. Is this a percentage increase or a decrease? [3] __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ c) What was the thickness of ice in May 1980 if the thickness is decreased by 28% from May 2021? [3] __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Question 6: Ben has deposited $10,000 into an American savings account paying 2% per week of compound interest to his deposit. Note that there are 52 weeks in a year. a) How much will he earn if he leaves his deposit in the account for 1 year? [3] __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ b) How much will he earn if the account was compounding continuously for 1 year? [3] __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ The formula for compound interest: π ππ‘ πΌ = π (1 + ) π
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