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Math 1350 Review #2(answers) 1. Write the equivalent Hindu-Arabic base ten numeral for each of the following numerals: a) b) CMXLIV (Roman) || (Egyptian) 32 944 c) (Mayan) d) (Babylonian) 121 6006 e) 10101two f) ETtwelve 21 142 2. Express the following in expanded form. a) 759 b) 2102three 7 100 5 10 9 c) 1E 4twelve 2 27 1 9 0 3 2 3. Find the missing base, if possible: a) 35 120b 1144 1112 4 b) 21six 27b 35 b 2 2b b 2 2b 35 0 12 1 2b 7 13 2b 7 b 7 b 5 0 2b 6 b 7 or 5 b3 5 But 7 isn't a digit in base three, so not possible 4. a) Express the following relation using ordered pairs: a b c d e a, c , b, c , c, a , c, d , d , a , d , e , e, b b) Does this relation have the symmetric property? No; b is related to c, but c is not related to b. c) Does this relation have the transitive property? No; b is related to c and c is related to d, but b is not related to d. d) Does this relation have the reflexive property? No; no element is related to itself. e) Is this relation a function? No; c is related to a and c is related to d. 5. a) Express the following relation using ordered pairs: a a b b c c d d e e a, a , b, b , b, a , c, c , d , c , d , d , e, e b) Does this relation have the reflexive property? Yes c) Does this relation have the transitive property? Yes d) Does this relation have the symmetric property? No; b is related to a but a is not related to b. 6. a) Express the following relation using ordered pairs: 1,1 , 1,2 , 1,3 , 2,1 2,2, 2,3, 3,1, 3,2 , 3,3 b) Does this relation have the reflexive property? Yes c) Does this relation have the symmetric property? Yes d) Does this relation have the transitive property? Yes e) Is this relation an equivalence relation? Yes f) Is this relation a function? No; 1 is related to 1 and 1 is related to 2. 7. For the set A 1,2,3,4 , consider the partition 1,2,3,4 . Write the equivalence relation generated by the partition as ordered pairs. 1,1 , 1,2 , 2,2 , 2,1 , 3,3, 3,4 , 4,4 , 4,3 8. a) Determine the common difference for the following arithmetic sequence: 5,1,7,13,19,25, The common difference is 6. b) Write a function of the form f n an b which generates the numbers in this arithmetic sequence. f n 5 6 n 1 f n 6n 11 c) Is 71 a number in this arithmetic sequence? 6n 11 71 6n 82 41 n 3 No 9. a) Determine the common ratio for the following geometric sequence: 1, 2,4, 8,16, 32, The common ratio is 2 b) Write a function of the form f n ar n1 which generates the numbers in this geometric sequence. f n ar n1 f n 1 2 f n 2 n 1 n 1 c) Is 512 a number in this geometric sequence? 101 2 512 Yes 10. Use the given operation table to find the result of the following operations: + A B C A C A B B A B C C B C A a) A C b) A A B c) A B d) A C B C A C 11. Consider the operation defined by the following table: + A B C A A B C B B C A C C B A a) Is the operation commutative? No; C B B but B C A b) What is the zero element? A 12. Which of the following sets are closed under addition? a) 0 b) 1,2 Closed Not Closed 0 0 0 0 1 2 3 1,2 c) 0,2,4,6,8,10,12, Closed adding multiples of 2 results in a multiple of 2 13. Complete the following addition table in base three: + 0 1 2 0 0 1 2 1 1 10 2 2 2 10 11 14. Which of the following sets are closed under multiplication? a) 1 b) 1,3 Closed Not Closed 1 1 1 1 3 3 9 1,3 c) 0,4,8,12,16,20, Closed The product of multiples of 4 will be a multiple of 4. 15. Complete the following multiplication table in base three: 2 0 1 0 0 0 0 1 0 1 2 2 0 2 11