Name : ______________________ ( ) Class: __________ Date: __________________ Fundamental Concepts & Set Theory - QUIZ Question 1: Suppose that : [13] 𝐴 = { 1 , 2 , 3 , 6 , 7 } , 𝐵 = { 4 , 7 , 12 , 2 , 3 } , 𝐶 = { 1 , 3 , 2 , 7 , 8 , 9 } , 𝐷 = { 7 , 3 , 1 , 2 , 6 } 𝜉 = ℤ Fill in the symbols ∈ , ∉ , ⊂ , ⊆ , ⊃ , ⊄ for the following: a) 𝐴 _____ 𝐷 b) { 4 , 7 , 12 } _____ 𝐵 c) 6 _____ 𝐶 d) { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 12 } _____ 𝐵 e) 7 _____ 𝐷 f) ∅ _____ 𝐶 g) 𝐴 _____ 𝜉 h) 𝐷 _____ ℝ i) 𝜉 _____ ℚ j) 30 _____ 𝜉 k) 𝐵 _____ 𝐷 l) 𝜉 _____ 𝐴 m) ℕ _____ 𝜉 Question 2: Please write down the cardinality of the following sets: [3] a) 𝐸 = { 1 , 4 , 1 , 2 } 𝑛 ( 𝐸 ) = ______ b) 𝐹 = { 1 , 2 , 3 , 5 , 8 } ∪ { 6 , 7 , 9 } 𝑛 ( 𝐹 ) = ______ c) 𝐺 = { 1 , 2 , 3 , 6 , 9 } ∩ { 7 , 12 , 5 , 1 , 6 } 𝑛 ( 𝐺 ) = ______ Question 3: The following questions are about set - builder notation: [6] a) Please write down this set into roster notation: 𝐻 = { 𝑝 𝑞 : 𝑝 , 𝑞 ∈ ℤ , 0 ≤ 𝑝 ≤ 2 , − 3 ≤ 𝑞 < 0 } __________________________________________________________________________________ _________________________________ _________________________________________________ b) Please rewrite this set into set - builder notation: 𝐾 = { 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 200 0. [2] __________________________________________________________________________________ __________________________________________________________________________________ b) After 21 years , the thickness of ice is now 1.8 metres. Fi nd the percentage change from M ay 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 in terest 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 muc h will he earn if the account was compounding continuously for 1 year ? [3] __________________________________________________________________________________ __________________________________________________________________________________ _ _________________________________________________________________________________ T h e formula for compound interest : 𝐼 = 𝑃 ( 1 + 𝑟 𝑛 ) 𝑛𝑡