Problem 3.4 (Grade a "Disproof"). Study the following claim as well as the "disproof": Claim. For all integers n, if 8{ n³ then 10{ n. "Disproof". Let n = 20, which is an integer. We see that 8 | 203 and 10 | 20. So n = 20 is a counterexample of the claim. Hence the claim is false. Complete the following questions concerning the above claim and "disproof": (1) Determine whether the "disproof " is valid. Identify the issues in the “disproof", if any. (2) Determine whether the claim is true or false. Justify the answer in part (3). (3) If the the claim is false and the "disproof" is not valid, then please provide a valid disproof/counterexample. If the claim is true, give a rigorous proof.

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