Are the following statements true or false?

? True False  1. Three nonzero vectors that lie in a plane in $R^3$ might form a basis for $R^3$.

? True False  2. If the set of vectors $U$ is linearly independent in a subspace $S$ then vectors can be added to $U$ to create a basis for $S$

? True False  3. If $\ S =$ span{$u_1, u_2, u_3$}, then $dim(S) = 3$ .

? True False  4. If the set of vectors $U$ spans a subspace $S$, then vectors can be added to $U$ to create a basis for $S$

? True False  5. If the set of vectors $U$ is linearly independent in a subspace $S$ then vectors can be removed from $U$ to create a basis for $S$.