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# Exam2ReviewAnswersinclcomb - Math 215 i Exam2 Name...

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Math 215 . i) Exam2 Name ':K.LUituJ AttZ;W{A S -- I 1) Define a relation, Ron Z by aRb if 51 a-b. Prove R is an equivalence relation. KeJ-l c 'f.-\ 1ft.- " 7rnv'R 0.. ,(C, . C:~ -0 ..... ~ a 5" I 0 ~' o--Kv ..... I S~{Y\(\~h<'- '. Assu-~ c<--K6 -I-~~Vl SIc- -la, So 'dj e-l s"t. ~j ::. k -\0 . -\ W 1'1 b- 4. == - LeA- - b) -=- ~ L ~J' '). .'. 5\6 -C-\., to K- e.. ·-to (l 5 (tA -b t\. V1 cC \ of <A Y\ '::, " t\ lAR .' A s Sv I"I'\J'.. CA K.- ~ 0'" V\. cL .. t 5'-0-.-6 t~cl ~ l 6 - c.. . l~ (1 Jj \ Ie ... -'= l 6 . J- Sk ~ \0 - L lAJ.,lU ~ - L- -:. (]A... - ~ j- to .. G -:::: S~ +- SIt--- =- ~(j t-IL ') Sl a - 2) What are the equivalence classes generated by the relation in problem # I? C3] L4] 3) Tell whether each of the following is an equivalence relation. If a relation is not an equivalence relation, tell which of the properties (Reflexive, Symmetric, Transitive) fails. a) Define R on the set of integers as follows: aRb if a < b. tlO t VR-~l~~ iv-t I no t- SJ VYlVY'--Q. 1v-I'C b) Let M={items on the menu at McDonald's}. Define aRb if a and b are both dessert items. f\~ (R.- f I ~'i-l'J'<.. .~ j Me"- L 7 IS j'j ;111 a. C- I'

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4) Write the degree sequence for the following graph: ( 0 I 0, 0/ f.tJ I 0 I 0 , ." J 5) Is the following an ISBN? Why or why not? 0-242-563-241 I LD) -\- ;).Lp

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