...My expertise covers a wide range of subjects, including IB Mathematics (SL and HL), Cambridge IGCSE, A Level, Pre Calculus, Calculus, NY Regents (Algebra I, Geometry, Algebra II), and SAT & ACT Math. I've also prepared students for challenging competitions like the Russian Regional Math Olympiad... (read more)
...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. Because (m, n) ? R-1, (n, m) ? R. Therefore, (m, n) ? R and (n, m) ? R. (read more)