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Determine all cosets of (19) in Uzo Show that Uzk19) is isomorphic to Z4...

Question

Determine all cosets of (19) in Uzo Show that Uzk19) is isomorphic to Z4

Determine all cosets of (19) in Uzo Show that Uzk19) is isomorphic to Z4



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Let f be an ordered field and x,y,z in F.
Prove that if x<0 and y<z, then xy>xz.

Reflexive and transitive than ours? Asymmetric. I think this is the most straightforward of the three Bruce. Okay, so uh let R. B. Your reflexive and transitive. Um oh let X Y bien are and now what I'm going to do is I'm going to suppose that Y X I suppose why X is in our then since our is transitive, X. X is in our and why why is in our but that's a contradiction are is mhm. It reflexive. So Y X. What I supposed right here cannot be in our and thus our is anti symmetric. Oh, no, no, no. Asymmetric, sorry. Yeah.

Hi. So um been able to look for to be able to side to sell for Z. Um let's just rewrite the equation down here. So we have more space. So to do this, what you want to do is use distributive property. And what you would do is you would simply um Distribute to W to the -4 As well as the two. So this becomes W our, sorry negative for W. Um So yeah, I either for W uh plus W. Z is equal to EMC plus 17. So then you notice how W. Z also has the same variable as MZ. So we want to get them on the same side but we want to move the negative four W. On this side. So it evens out. So to do that, what you want to do is um use inverse operation. So you would add for Um at four W on this side. Yeah. And that cancels out because negative four plus four is zero and you want to do that to the other side because what you do to one side the equal sign yet did you to the other and then you want to subtract EMC on this side. Just think of this as 1 -1. Um Medical zero. And then you want to I'm just going to put this right here. Kind of actually I can delete this because it becomes negative MZ. On this side. So now you're kind of left with this and I will delete this kind of less confusing. So now you're loved with MZ um one second. Sorry I am negative MZ Plus W. C. Is equal to 17 plus four W. So the next thing you want to do is go through the process of something called Factory Ization. And what that basically does is we're gonna take this um expression here and we are going to kind of break it down. So it looks like distributive property. Just like we did with the W um times 94 W times E. So we both see that Z is in um is the same variable in both of these. So you want to start off easy and in parentheses put W minus M. So that when you look like when it looks like you are doing um distributive property, it would turn into the same W. Z. And negative MZ. And then we can obviously keep the right side of the equation. So this is a really bad for, sorry um for W 17 Plus four W. Now to get Z alone, we want to divide bye. W minus M. So this is saying um Z times W minus M. So the opposite of multiplication is division. So we want to divide over W minus M. So that cancels out and divide Bye. Tell you minus. Um So when you simplify that, alter or sign up supply, when you kind of clear all that together, you get Z equals 17 plus four W over W minus M. Thank you so much for the question. If you have any confusion to let me know, I'd be more than happy to help you and I hope you have a great rest of your day. Thank you.

Hello. Real question. Envisages when that F B and ordered field and X. So I said enough. Okay. It has also given that if X less than zero and why less than that then we need to prove that X. Y greater than access it. So let us get to hear that if access less than zero, this can be written as minus Act should be greater than zero. Okay, now here, if y is less than that so Zach minus Y should be greater than zero. Okay, no, these two have become positive quantities. Some multiplication of two positive quantities should be always positive, should always be positive. So we stretch it as minus X. Which is a positive quantity. Now into that minus Y. Which is again a positive wants to know should be positive. Let us open the bracket minus X. Z bless X. Y should be positive. Let us add except to both the sides will be having X way this is minus exceed all. It is minus except plus X. Y. And we are adding acceptable the sides greater than exit. So these two will become zero. So from here we are getting X. Y greater than X zet. So this is the thing we need to prove. Thank you.

Hello. Real question. Envisages when that F B and ordered field and X. So I said enough. Okay. It has also given that if X less than zero and why less than that then we need to prove that X. Y greater than access it. So let us get to hear that if access less than zero, this can be written as minus Act should be greater than zero. Okay, now here, if y is less than that so Zach minus Y should be greater than zero. Okay, no, these two have become positive quantities. Some multiplication of two positive quantities should be always positive, should always be positive. So we stretch it as minus X. Which is a positive quantity. Now into that minus Y. Which is again a positive wants to know should be positive. Let us open the bracket minus X. Z bless X. Y should be positive. Let us add except to both the sides will be having X way this is minus exceed all. It is minus except plus X. Y. And we are adding acceptable the sides greater than exit. So these two will become zero. So from here we are getting X. Y greater than X zet. So this is the thing we need to prove. Thank you.


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