Michael Sipser Edition 3 Exercise 4 Question 15 (Page No. 212)

Question

Show that the problem of determining whether a CFG generates all strings in $1^{\ast}$ is decidable. In other words, show that $\{\langle { G \rangle} \mid \text{G is a CFG over {0,1} and } 1^{\ast} \subseteq L(G) \}$ is a decidable language.