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Consider the following inductive sets: 1. Nat is the inductive at defined by the following constructors: a. Zero : Nat. b. Suc: Nat Nat. 2. Var is the inductive set defined by the following constructors: a. X: Nat Var. b. Y: Nat Var. 3. Term is the inductive set defined by the following constructors: a. V: Var Term. b. C: Term. c. F: Term Term 1. Form is the inductive set defined by the following constructors: a. Eq: Term x Term Form. b. Neg: Form Form. c. Imp: Form x Form Form. d. All : Var x Form Form. The members of Form represent the formulas in a first-order language. Prove that Form is countably infinite. Hint: Use Gdel numbering to assign a unique natural mimber to each member of Form. Consider the following inductive sets: 1. Nat is the inductive at defined by the following constructors: a. Zero : Nat. b. Suc: Nat Nat. 2. Var is the inductive set defined by the following constructors: a. X: Nat Var. b. Y: Nat Var. 3. Term is the inductive set defined by the following constructors: a. V: Var Term. b. C: Term. c. F: Term Term 1. Form is the inductive set defined by the following constructors: a. Eq: Term x Term Form. b. Neg: Form Form. c. Imp: Form x Form Form. d. All : Var x Form Form. The members of Form represent the formulas in a first-order language. Prove that Form is countably infinite. Hint: Use Gdel numbering to assign a unique natural mimber to each member of Form