Hello my name is Kionna! I graduated with my Bachelor's and Master's degrees from Syracuse University. I am certified in general education grades 1-6 and special education grades 1-12. (read more)
3 Subjects: includingPrealgebra,Elementary (K-6th),Elementary Math
Hello! My name is Andy - I am an 11-year veteran of the U.S. Navy Submarine Force, and have since worked with both defense contractors and commercial nuclear power plants. (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)