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Which of the following statements is inc...

Which of the following statements is incorrect ?

A

Every integer is a rational number

B

Reciprocal of zero is not defined

C

The product of two rational numbers is always a rational number.

D

Every negative rational number is greater than zero.

Text Solution

AI Generated Solution

The correct Answer is:
To determine which statement is incorrect, we need to evaluate each of the provided statements one by one. ### Step-by-Step Solution: 1. **Evaluate the first statement**: "Every integer is a rational number." - **Explanation**: An integer can be expressed as a fraction where the denominator is 1 (e.g., 3 can be written as 3/1). Since all integers can be expressed in this form, this statement is **true**. 2. **Evaluate the second statement**: "0 is equal to 1 upon 1." - **Explanation**: The fraction 1/1 equals 1, not 0. Therefore, this statement is **false**. 3. **Evaluate the third statement**: "The product of two rational numbers is always a rational number." - **Explanation**: If we take two rational numbers, say a/b and c/d, their product is (a/b) * (c/d) = (a*c)/(b*d). Since both a, b, c, and d are integers and b and d are not zero, the product is also a rational number. Thus, this statement is **true**. 4. **Evaluate the fourth statement**: "Every negative rational number is greater than zero." - **Explanation**: A negative rational number, such as -2, is indeed less than zero. Therefore, this statement is **false**. ### Conclusion: After evaluating all the statements, we find that: - The first statement is true. - The second statement is false. - The third statement is true. - The fourth statement is false. The incorrect statements are the second and fourth. However, since the question asks for one incorrect statement, we can conclude that the **second statement** is the most straightforwardly incorrect. ### Final Answer: The incorrect statement is: "0 is equal to 1 upon 1." ---
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