Consider the proof provided below. Determine if the proof given is valid, and if

Question

Consider the proof provided below. Determine if the proof given is valid, and if so, which method of proof is being employed. The proof is valid and it is a direct proof. The proof is valid and it is a proof by contrapositive. The proof is valid and it is a proof by contradiction. This is not a valid proof. The proof is valid, but it uses a method different from those listed above. Statement: If x is an irrational number, then x^1//3 is also irrational. Proof: Suppose that x^1/3 is rational. Then there exist integers a and b, with b notequalto 0, such that x^1/3 = a/b. Then, x = (a/b)^3 = a^3/b^3. Hence, since a^3 and b^3 are integers, x is rational. Thus, the statement is proved.

Explanation / Answer

the proof is valid and is proved by contradiction

so the answer is c

the reason to it is because here the author goes onto to prove x as an rational number instead of irrational number.

proofs of this kind where one starts with a true belief and in the end proofs his belief as false is called proof by contradiction

well here the author uses

"Fermat's Last theorem to prove by contradiction"

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