ComputerScienceExpert

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Applied Sciences,Calculus,Chemistry,Computer Science,Environmental science,Information Systems,Science Hide all
Teaching Since: Apr 2017
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  • MBA IT, Mater in Science and Technology
    Devry
    Jul-1996 - Jul-2000

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  • Professor
    Devry University
    Mar-2010 - Oct-2016

Category > Programming Posted 09 May 2017 My Price 9.00

ECS20Homework 6Exercise

Can you explain how to do problems 4 and 5 on my discrete math homework?

 

ECS20Homework 6Exercise 1Prove or disprove each of these statements about the floor and ceiling functions.a)x⎢⎣⎥⎦⎡⎢⎤⎥=x⎢⎣⎥⎦for all real numbersx.b)xy⎢⎣⎥⎦=x⎢⎣⎥⎦y⎢⎣⎥⎦for all real numbersxandy.c)⎡ ⎤⎣ ⎦⎣ ⎦xx=for all positive real numbersx.Exercise 2Show thatx3isO(x4)but thatx4is notO(x3).Exercise 3a)Show that2x-9isΘ(x).b)Show that3x2+x -5isΘ(x2)c)Show thatx+23⎢⎣⎢⎥⎦⎥isΘ(x)d)Show thatlog10(x)isΘ(log2(x))Exercise 4Letaandbbe two integers. Use a proof by contradiction to show that ifa2-b2+2abis oddthena-bis odd.Exercise 5Use a proof by contradiction to show that:There exists a strictly positive real numberrsuch that for all real numberx, ifx−x⎢⎣⎥⎦<rthen3x⎢⎣⎥⎦=3x.Extra credit:We call a positive integer perfect if it equals the sum of its positive divisors other thanitself.a)Show that 6 and 28 are perfectb)Show that2p-1(2p-1)is a perfect number when2p-1is prime.

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ComputerScienceExpert
(11)
Status NEW Posted 09 May 2017 08:05 AM My Price 9.00

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