...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. I will happily provide recommendations from my former students upon request. (read more)
...It will now be shown that if R on A is antisymmetric, R n R-1 ? {(a, a): a ? A}. Let m, n ? A. Suppose that R on A is antisymmetric. Let R = {(m, n): m, n ? A}. Therefore, by definition of inverse relation, R-1 = {(n, m): m, n ? A}. Let (m, n) ? (R n R-1). By definition of intersection, (m, n) ? R and (m, n) ? R-1. (read more)