2. [5 points] Consider the orthogonality relation R on the set B3(0,0,0), (1,0,0), (0,1,0), (1,1,0), (0,0,1), (1,0,1), (0,1,1), (1,1,1)}, given by (X1, X2, X) R (Yu Yo ys) (Xyy? + X2Y2 + ????) mod 2-0, for all (X1, X2, X3), (y?, y2, y3) ? ? (a) Arque that R is symmetric. at is nottransitive, i.e., find some (Xu X2 %) (y?, ??, ??), and (zi, Z2, Zs) such that (X1, X2, X3) ?s orthogonal to (Yu Yo ys) and (y?, ??, ??) is orthogonal to (z?, Z2, Zs), but (X1, x2, x3) is not orthogonal to Z1, Z2, Z3