...The following is a proof done by me on antisymmetric relations, followed by a shorter proof on set intersection of set differences. Set notation is displayed as "?" on this site, obscuring details
A relation R on a set A is antisymmetric if and only if R n R-1 ? {(a, a): a ? A}.
It will f... (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 am a New York State certified Mathematics Teacher (grades 7-12) and currently work as an associate consultant for Weaver Recovery Consulting, an emergency management company. I graduated with a Bachelor's degree from SUNY Oswego in 2014. I double majored in Physics (B.S.) and Mathematics (B.A.) and acquired a cumulative GPA of 3.76. (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)