A vector space V and a subset S are given. Determine if S is a subspace of V, and if so, prove it. If not, give an example showing one of the conditions of Definition 7.3 is not satisfied.

DEFINITION 7.3 b Subspace A subset S of a vector space V is a subspace if 3 satises the following three conditions: (a) S contains 0, the zero vector. (b) If 11 and v are in S, then u + v is also in S. [:c) If c is a scalar and v is in S, then cv is also in S. \f