Download CPSC 121 – Tutorial Week 8 1. Translate the following theorems

CPSC121–TutorialWeek8
1. Translatethefollowingtheoremsintopredicatelogic,andthenprovethem.Youmayutilizethe
followingpredicates:Even(x),Odd(x),Square(x),Prime(x)
a. Theproductofanythreeconsecutiveintegersisdivisibleby6.
b. Iftwonumbersareperfectsquaresthentheirproductisaperfectsquare.
c. Foreverydistinctpairofrealnumbers,thereisanotherrealnumberbetweenthem.
d. Thereisexactlyoneevenprimenumber
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2. Prove that for every distinct pair of positive rational numbers and , the number
lies
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between and .Hint,withoutlossofgenerality,youcanassume > ,andthata,b,c,andd
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areallpositive.Ingeneral,agoodwaytoprovethatxisgreaterthanyistoshowthat𝑥 − 𝑦 = 0
3. Extraproblem-TranslatethefollowingsentenceintoEnglish,giventhefollowingdefinitions:
i. P
domainofallpeople
ii. K(x,y) personxknowspersony
iii. L(x,y) personxislivingincountryy
“EverypersonlivinginCanadaknowssomebodywhoknowsnobodylivinginBrazil”