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Integers: Prime Numbers

Is $$\sqrt[3]{{x}}$$ non-negative? >(1) The product of $$x$$ and positive integer $$y$$ is not $$x$$. >(2) $$x$$ is a prime number.
Incorrect. [[snippet]] According to Stat. (1), the product of $$x$$ and positive integer $$y$$ is not $$x$$. Notice that we know nothing of $$y$$, but we don't really care. Actually, $$y$$ is of no great importance here; it's only utility is in telling us something about $$x$$. The only number that would be equal to itself when multiplied by any other number is 0. Thus, what this sentence actually means is that $$x$$ is not 0. Since the only thing this statement tells us is that $$x$$ isn't 0, $$x$$ can still be any other number. Try plugging different values for $$x$$. Remember to check both positive and negative numbers, just to be safe. Also, plugging in numbers which actually have an integer third root will make things easier: * If $$x=8$$, then $$\sqrt[3]{x}=2$$, which is non-negative, so the answer is "Yes." * If $$x=-8$$, then $$\sqrt[3]{x}=\sqrt[3]{-8}=-2$$, which is negative, so the answer is "No." Therefore, the answer is "Maybe," and **Stat.(1) → IS → BCE**.
Incorrect. [[snippet]] According to Stat. (1), the product of $$x$$ and positive integer $$y$$ is not $$x$$. Notice that we know nothing of $$y$$, but we don't really care. Actually, $$y$$ is of no great importance here; it's only utility is in telling us something about $$x$$. The only number that would be equal to itself when multiplied by any other number is 0. Thus, what this sentence actually means is that $$x$$ is not 0. Since the only thing this statement tells us is that $$x$$ isn't 0, $$x$$ can still be any other number. Try plugging different values for $$x$$. Remember to check both positive and negative numbers, just to be safe. Also, plugging in numbers which actually have an integer third root will make things easier: * If $$x=8$$, then $$\sqrt[3]{x}=2$$, which is non-negative, so the answer is "Yes." * If $$x=-8$$, then $$\sqrt[3]{x}=\sqrt[3]{-8}=-2$$, which is negative, so the answer is "No." Therefore, the answer is "Maybe," and **Stat.(1) → IS → BCE**.
Incorrect. [[snippet]] According to Stat. (2), $$x$$ is a prime number. Remember, prime numbers are positive by definition, so according to this statement, $$x$$ must be positive. As long as $$x$$ is positive, its third root is also positive. This means $$\sqrt[3]{x}$$ is always non-negative, and the answer is "Yes," so **Stat.(2) → S → BD**.
Incorrect. [[snippet]] According to Stat. (2), $$x$$ is a prime number. Remember, prime numbers are positive by definition, so according to this statement, $$x$$ must be positive. As long as $$x$$ is positive, its third root is also positive. This means $$\sqrt[3]{x}$$ is always non-negative, and the answer is "Yes," so **Stat.(2) → S → BD**.
Correct. [[snippet]] According to Stat. (1), the product of $$x$$ and positive integer $$y$$ is not $$x$$. Notice that we know nothing of $$y$$, but we don't really care. Actually, $$y$$ is of no great importance here; it's only utility is in telling us something about $$x$$. The only number that would be equal to itself when multiplied by any other number is 0. Thus, what this sentence actually means is that $$x$$ is not 0. Since the only thing this statement tells us is that $$x$$ isn't 0, $$x$$ can still be any other number. Try plugging different values for $$x$$. Remember to check both positive and negative numbers, just to be safe. Also, plugging in numbers which actually have an integer third root will make things easier: * If $$x=8$$, then $$\sqrt[3]{x}=2$$, which is non-negative, so the answer is "Yes." * If $$x=-8$$, then $$\sqrt[3]{x}=\sqrt[3]{-8}=-2$$, which is negative, so the answer is "No." Therefore, the answer is "Maybe," and **Stat.(1) → IS → BCE**. According to Stat. (2), $$x$$ is a prime number. Remember, prime numbers are positive by definition, so according to this statement, $$x$$ must be positive. As long as $$x$$ is positive, its third root is also positive. This means $$\sqrt[3]{x}$$ is always non-negative, and the answer is "Yes," so **Stat.(2) → S → B**.
Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.