let $S$ and $T$ be two subspaces of $R^{24}$, such that $\dim(S)= 19$ and $\dim(T)= 17$, then the
a. Smallest possible value of $\dim(S \cap T)$ is ?
b. largest possible value of $\dim(S \cap T)$ is ?
c. Smallest possible value of $\dim(S + T)$ is ?
d. largest possible value of $\dim (S + T)$ is ?