Problem of Induction

Read Goodman's "New Riddle" and please answer the following questions (minimum of 500 words):
What is the “old problem” of induction?
According to Goodman, how can one show that a rule of inference is justified?
What is the “new problem” of induction?
Define “x is grue.”
According to Goodman, is the sentence “All emeralds are grue” projectible?
What about the sentence “All emeralds are green”?

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