(a) If vectors u, v, and w are linearly independent, will u + v, v + w,...

Question:

(a) If vectors u, v, and w are linearly independent, will u + v, v + w, and u + w also be linearly independent? Justify your answer.
(b) If vectors u, v, and w are linearly independent, will u - v, v - w, and u - w also be linearly independent? Justify your answer.