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A relation R on a set A is antisymmetric if and only if R n R-1 ? {(a, a): a ? A}.
It will first be shown that if R n R-1 ? {(a, a): a ? A}, R on A is antisymmetric. Suppose R n R-1 ? {(a, a): a ? A}. Let R = {(x, y): x, y ... (read more)
...Thank you for your consideration!I successfully completed Regents exams in Mathematics, Physics, US History, and English, earning a NY Regents High School diploma in 1999. Since then I attended the U.S. Naval Academy, majoring in Systems Engineering, and have served 10 years as a Navy Nuclear Submarine Officer. (read more)
...I have two children now in college, at Ivy League schools. I was their primary caregiver throughout their childhood, and helped them with their schoolwork whenever they needed it. They both took math up through AP calculus (one of them took Calculus BC). One of them took AP Chemistry, the other took AP Physics, so I have seen some of the work done in those classes. (read more)
...I completed my Master's in mathematics education from Syracuse University and I am currently a PhD candidate in mathematics education on track to complete my PhD in July 2024. My teaching methodology is focused on making mathematics accessible and relevant to students from diverse backgrounds b... (read more)