1. (10 points) Recall the inductive definition of [operation involving strings redacted]: Base Case: (redacted] Inductive Case: (redacted] Prove that [property of the string operation redacted). You may only use basic logic, the inductive definition of (redacted] given above, and the fact that the string concatenation operation is associative with two-sided identity (i.e., eu = u = u for any string u). You may regard a single symbol as a string of length 1. 1. (10 points) Recall the inductive definition of [operation involving strings redacted]: Base Case: (redacted] Inductive Case: (redacted] Prove that [property of the string operation redacted). You may only use basic logic, the inductive definition of (redacted] given above, and the fact that the string concatenation operation is associative with two-sided identity (i.e., eu = u = u for any string u). You may regard a single symbol as a string of length 1