...Therefore, (m, n) ? R and (n, m) ? R. Since by definition of antisymmetric, (mRn ? nRm) implies m = n, then m = n. Notice that m and n are equal elements of A, and that (m, n) ? (R n R-1). Therefore, ? (m, n) ? (R n R-1), (m, n) ? {(a, a): a ? A}. Thus, by definition of subset, (R n R-1) ? {(... (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)
...Naval Academy, and a Master of Education degree from Norwich University. I achieved perfect math scores of 800 on both the SAT and the GRE. I have tutored many students, especially in NY high school Regents math and science courses, as well as college calculus and calculus-based physics, and I truly enjoy sharing my methods of understanding these subjects with others. (read more)