(a) Prove that n + 2n is divisible by 3 for each n EN.(b) Let z = sin 1 (in radians) and let y = v2. Prove that the following statement is false:(z+ y € Q) A (1- y E Q).(c) Let ai = 1 and let a2 = n. For n > 3, we define recursively an = an-2 – an-1. Is it true thata2021 is rational? Prove that your answer is correct.

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Prove that n + 2n is divisible by 3 for each n eN. Let z = sin 1 (in radians) and let y = v2. Prove that the following statement is false: (z+ y € Q) A (r- y e Q). Let a = 1 and let az = . For n 2 3, we define recursively an = an-2- an-1. Is it true that a2021 is rational? Prove that your answer is correct.