My name is John. I am a 68 year old retiree who enjoys working with high school students to improve their algebra and geometry skills. I have been doing on-line tutoring for 4 years and believe I’ve helped several students improve their grades while also keeping my own cognitive skills refreshed in retirement. (read more)
...I believe that learning is about the whole person. The important thing to me is seeing how what you learn helps you grow. Even if you are struggling with a difficult and dreaded subject, I try to show how you can be successful and feel good about your learning. (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)