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Exercise 6.6. Let the inductive set be equal to all natural numbers, N. Prove the following...

Exercise 6.6. Let the inductive set be equal to all natural numbers, N. Prove the following propositions. (a) ∀n, 2n ≥ 1 + n.

(b) ∀n, 4n − 1 is divisible by 3.

(c) ∀n, 3n ≥ 1 + 2 n.

(d) ∀n, 21 + 2 2 + ⋯ + 2 n = 2 n+1 − 2.

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