For option, C

"Note that L(G) != φ if and only if G’s start variable can generate a string in T∗, where T is G’s terminal alphabet. We simply determine this property for each variable A in G : can A generate a string in T∗ ?"

For option, D found this

Note that L(G) is infinite exactly if there is a path in a derivation tree with a repeated variable. The following algorithm identifies the variables that can be repeated in this way; L(G) is infinite exactly if there is at least one such variable

From- https://cs.nyu.edu/courses/fall09/V22.0453-001/chapter-4.pdf 4.4.3 & 4.4.6 Example.