Consider the orthogonality relation R on the set B^2 = {(0,0), (1,0), (0,1), (1,1)}, given by (x1, x2) R (y1, y2) ⇔ (x1·y1 + x2·y2) mod 2 = 0, for all (x1, x2),
(y1, y2) ∈ B^2.
(a) Show an example of a relation matrix MR representing R.
(b) Is R reflexive? symmetric? antisymmetric? transitive? Explain your answers.