Math 245-Test_2(Summer 2020).doc - MATH 245- Test#2...

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MATH 245- Test#2 (ZAHEDANI)Summer 2020PCC…………………………………………Name……….……………………Answer at least ten questions1)For the universal set U and the given sets1,2,3,4,5,6,7,8,9,10 ,1,3,5 ,1,2},2,5}UABC, verify that the followingidentities hold by calculating each side of the equation separately.a)()cccABABb)()()()ABACABC2)For the given sets:, ,,,},, }Aa b cBa dCd c, verify that the following identitieshold by calculating each side of the equation separately.a)()()()ABCABACb)()()()ACABABC
3)Suppose you save money at a bank that pays 4% per year in simple interest. If you openthe account with $500, and in addition to the interest that the bank pays, on the last dayof each year, you deposit $100 more into the account. Give a recurrence relation for)(nS, your money at the end of n years, for0n. How much money will you haveat the end of 4 years?4)Use induction method to solve115,1nnaaafor all integers2n.
5)Let120156,0,1nnnaaaaa.Use strong induction to show that for all,0n32nnna6)Solve the linear recurrence relation1201710,0,3nnnaaaaa7)Solve the linear recurrence relation
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Term
Fall
Professor
smith
Tags
Recursion, Recurrence relation

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