...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) ? {(a, a): a ? A}. Therefore, if R on A is... (read more)
...The tutoring experience shifted my career goal to become a teacher. I taught middle and high school mathematics for 5 years and decided to pursue a graduate degree. 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. (read more)