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Part MIQuestion 3. You know that 56 = -8 (mod 27). Find 5'2,5I8 and 52018 modulo 27.Question 4 Define f 22 R' by f(y) = (1+9.2x-Y+I+2). Determine whether ...

Question

Part MIQuestion 3. You know that 56 = -8 (mod 27). Find 5'2,5I8 and 52018 modulo 27.Question 4 Define f 22 R' by f(y) = (1+9.2x-Y+I+2). Determine whether one-tO-onle _ onto, both_ or neitherQuestion 5. Define $ R~Rbyif x < 0, if x =0. if x > 0.s(x) =(a) For an open interval (a,b) in R, find its preimage $-'((a,b)). (b) Using the definition of continuity in terms of preimages, explain why is not continuous.Question 6 relation is defined on R by: X ~ > if and only if xy 2 0

Part MI Question 3. You know that 56 = -8 (mod 27). Find 5'2,5I8 and 52018 modulo 27. Question 4 Define f 22 R' by f(y) = (1+9.2x-Y+I+2). Determine whether one-tO-onle _ onto, both_ or neither Question 5. Define $ R~Rby if x < 0, if x =0. if x > 0. s(x) = (a) For an open interval (a,b) in R, find its preimage $-'((a,b)). (b) Using the definition of continuity in terms of preimages, explain why is not continuous. Question 6 relation is defined on R by: X ~ > if and only if xy 2 0. Is this relation an equivalence relation? If is not an equivalence relation, which of the required properties does it have and which does it fail to have?



Answers

a) Let $R$ be the relation on the set of functions from $\mathbf{Z}^{+}$ to $\mathbf{Z}^{+}$ such that $(f, g)$ belongs to $R$ if and only if $f$ is $\Theta(g)$ (see Section $3.2 ) .$ Show that $R$ is an equivalence relation.
b) Describe the equivalence class containing $f(n)=n^{2}$
for the equivalence relation of part (a).

You were asked to be turgid following relation on the set of function, the transformation from into yours. And if you are a couple information the function of one. The function that one is the ability to function devaluated one well, one could achieve one. If that's the commission, then it's clearly reflecting symmetric and transitive. Everything inside said is all the same. So a and and equivalence relation I'm gonna call You are And it would be We have this set We have the same thing We have comedy where f of zero z good g a year or one is with you GF one Well, you can you can already see that, not transitive. So if you have that one euro equals zero and in years to have g of one Coors P of one, then you have after the zero ico p of zero and from one p of one, it's not transitive or here. So you can have when you wanted the one of the police being true at a time you could have yeah, and in for TV have that where affects my lead to one for always Call me G. We're because even if you do that for all in the well, it's actually pretty easy. Next, my dear. No, sorry he has affects. My next year is equal to one for all in the well. You have a Rolex, my sex that 30 It's not one, so it's not reflective. We take their relation on if you have, then you get that's like my that's like, which is obviously in a zero, and it's not even someone should be equal one that implies it's not reflective, like asking, not be related itself and report. Devi has said ecology and for some he in the we're told for some scene. We I'm not worried. Dirt just seen the such that for all the I have my next year. If you were given well, let's check in with reflection she has. Really? Then you get up. My nephew people zero. So there exists. Some seeing V is there inside the intruders, so that works. Reflexive reflective. Let's check of its metrics of official ated Teoh G. And that implies do you of a pill if other next my GF. Then first week gives us my because some see and in do you like my back. Give the university Have you? Both sees are in the to see the one or inside the singers. That implies it's symmetric. His condition is that there exists some see and your phone Q C. Here C, C and C one they're built inside in two years. So that implies symmetric the chicken trendy If you have escalated Teoh G in DE later to you p that employees after related p don't be. Is that true? She had a my it was something on he had like my Pierre because the letter c and then you have minus here legally limiters he for all three d c. Either inside the uh to all I are inside the that implied it's transitive because those the condition we needed having see that inside No check he lost that. They give that e you were told we have a comedy. What's that? After zero g of one. And what if you could give zero? So let's check Reflective reflection really applies. That official waited up right? So we have that implies zero you could g of euro. You get the upper one and that would g of one. Oh, I would, but you can have being function where zero gives you some number and half of one gives you a different number. The so you you can have. Where after euro might not be eager to have one. It's not. It's not reflective, and therefore it's not in the equivalence relation. The only a cripple information we got were in the and the rest without equivalence relation.


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