Let V be a vector space and let W1 and W2 be subspaces of V. Define the following subsets of V: W1 + W2 = {w1 +w2 | w1 W1 and w2 W2} W1n W2 = {w V | WE W1 and w W2} W1 UW2 = {W EV | W e W1 or we W2} (a) Show that W1n W2 is a subspace of V. (b) Show that W1 + W2 is a subspace of V. (C) Let V = R 2. Show by means of an example that W1 U W2 is not necessarily a subspace of R 2. Which of the three rules is not satisfied?