Proof

\end{lemma} \noindent Proof: $\tilde{I}_n \subseteq I_n$ since $Z_n \in P_n$. Remains to prove that $T_n \subseteq \tilde{I}_n$ and $P_n \subseteq \tilde{I}_n$. \\[5pt] $x_1 z_1$ is congruent to $x_1 (x_1 y_1 + x_1 + y_1) = x_1^2 y_1 + x_1^2 + x_1 y_1$ mod $(L_n)$, which is congruent to $x_1 y_1 + x_1 + x_1 y_1 = x_1$ mod $(S_n)$. Since $L_n$ and $S_n$ are in $\tilde{I}_n$, one sees that $x_1 z_1$ is congruent to $x_1$ mod $\tilde{I}_n$ and so $x_1 z_1 - x_1 \in \tilde{I}_n$. The same proof…

standard is right. With an analytical and qualitative approach, Knizet compares Sael v. Ashcroft with Lie v. Ashcroft. She looks at the principles in the Refugee Act, INS v. Cardoza-Fonesca and INS v. Kotasz, human rights law, and explains the burden of proof tests. Both Lie and Sael applied for asylum fearing further persecution by the majority population in Indonesia because of their Chinese Christian identities.…

Torvald said: “You don’t feel as if you could believe that I have forgiven you. But it's true, Nora I swear it; I have forgiven you everything” (Henrik Ibsen 64) This is proof that he eats her lied about what he said to Nora before he got the letter or that he did not actually apologize and just lied to make everything go back to…

You’ll also need proof that you completed the required credit-counseling course. When the bankruptcy court clerk has accepted the paperwork, you receive an official court stamp and case number that confirms the filing. Next you need to touch base with your employer. In…

Cheryl. Police eventually arrested them and the daycare was closed in 1984. Accusations are defined as claims that someone has done something wrong or illegal; therefore, they have to be proven. During the trials the only set of evidence they used as proof were child testimonies. Children from ages 3 to 7 are still figuring out the difference between fantasy and reality. They create imaginary worlds in their play(Hartwell-Walker). This was due to the hysteria. The fear the people lived in on a…

Figure 2.1 is a polygon with 12 sides. The polygon is not convex, as there is at least one reex angle. The objective of the art gallery problem is to hire the most efficient number of guards required to have vision of each point inside of the polygon. Begin with the process of vertex guards. The most visually optimal way to prove the result _n 3 _ is by first triangulating the polygon. Every vertex of the polygon can be attached in such a way that the entire polygon is made up of solely…

The narrator in The Wife’s Story can be trusted because in her eyes she is innocent, she was only doing what she needed to in order to save her pack. There is proof within the story that the narrator is the alpha female of the pack. One piece of evidence of this is “Lodge Meeting nights, more and more often they had him to lead the singing.” This proves that the narrator is alpha female because she is the mate of the wolf who is leading the howls, which is done by the alpha, not to mention, only…

solve this Global Warming problem because around the world there are many different people with many different traits , and if people come together we can solve this problem of Global Warming. The style that Gore uses is clear and he uses facts to proof how Global Warming is getting worse such as : India received record rainfall, or more than two cities in the United States broke all time heat records.…

The court of appeals put aside Evans conviction, because his oral admission should be used as evidence against him, nonetheless sustained the defendant ‘s conviction after the judge specifically told the jury that while Evans' admission was skillful proof against Evans, it was forbidden noise against respondent…

The author of this essay argues that public shaming can make people regret their actions and even become a good person. Because nobody likes to be publicly humiliated, people who committed a crime would change their bad behavior. However, this idea is not applied on the real world. The majority of criminals find some other people to be blamed for their mistakes. Therefore, making people feel shameful does not solve the issue because the guilty person keeps making excuses to not feel guilty about…