Consider the following inductive sets: 1. Nat is the inductive set 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. 4. 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 number to each member of Form. Consider the following inductive sets: 1. Nat is the inductive set 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. 4. 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 number to each member of Form