I am having trouble understanding the answers to the following two questions:

- If vector u, v, and w are linearly independent, will u+v, v+w, and u+w also be linearly independent?
- If vector u, v, and w are linearly independent, will u-v, v-w, and u-w also be linearly independent?

I know the answer to the first question is yes, and I know the answer to the second question is no, but I don't know why. Can someone provide me with an explanation. I can't come up with any justifications.