Consider the proof provided below Determine if the proof giv

Consider the proof provided below. Determine if the proof given is valid, and if so, which method of proof is being employed. A. The proof is valid and it is a direct proof. B. The proof is valid and it is a proof by contrapositive. C. The proof is valid and it is a proof by contradiction. D. This is not a valid proof. E. 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: Let x be an irrational number, and 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. This disagrees with our assumption that x is irrational. Thus, it must be that x^1/3 is also irrational.

Solution

Option : C

Proof is valid and it is a proof by contridiction