...I believe that tutoring can benefit every student regardless of their background in the topic or their current status. I'm looking forward to helping you achieve your goals!I have 3+ years of experience tutoring psych and my bachelor's degree in psychology. Hi! (read more)
...Suppose R n R-1 ? {(a, a): a ? A}. Let R = {(x, y): x, y ? A}. By definition of inverse relation, R-1 = {(y, x): x, y ? A}. By definition of subset, if (x, y) ? R n R-1, (x, y) ? {(a, a): a ? A}. Hence, x = y, and so (x, y) ? R implies (y, x) ? R. Since x = y, ? (xRy ? yRx), x = y. Thus, by definition of antisymmetric, R on A is antisymmetric. (read more)