Determine whether each of the following statements about events X, Y, Z is always true or not.

1. Suppose that X, Y, and Z are mutually exclusive events; then X^c (X complement) and Y U Z^c are mutually exclusive. (T/F)
2. From now on, we do not assume that X, Y, Z are mutually exclusive. Suppose that X is independent of Y, given Z.
(a) X^c is independent of Y, given Z. (T/F)
(b) X∩Z is independent of Y∩Z, given Z. (T/F)
(c) X is independent of Y,given Z^c. (T/F)