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Michael Sipser Edition 3 Exercise 4 Question 14 (Page No. 211)

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Let $\Sigma = \{0,1\}$. Show that the problem of determining whether a $CFG$ generates some string in $1^{\ast}$ is decidable. In other words, show that $\{\langle {G \rangle}\mid \text{G is a CFG over {0,1} and } 1^{\ast} \cap L(G) \neq \phi \}$  is a decidable language.
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Michael Sipser Edition 3 Exercise 4 Question 4 (Page No. 211)
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Michael Sipser Edition 3 Exercise 4 Question 28 (Page No. 212)
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