6. (Boolean algebra) a. Consider a boolean algebra over a set T. For each of the following, either prove that the equation is true for all x, y E T or give a counterexample. i. (y + x) + y' = x + y + (x' .y') ii. x' + (y x) = x + y iii. (x' y) + y' = x' + y' iv. x' + (x - y) = x' V. x. (y' + x') = x y' vi. x' .(y + x') = x' .y According to your solution to Exercise 6a, which of the following equations are true for all x, y E T? Select one or more: o (y + x) + y = x + y + (x' .y) x' (y + x') = x' y None of the other statements are true. x' + (y x) = x + y O X(1 + x) = xy