Questions: Determine whether the following statement is true or false. The product of two negative real numbers is positive. Choose the correct answer below. A. False, because the product of two negative real numbers is negative. B. True, because the product of two real numbers is always positive. C. True, because the product of two real numbers with the same sign is always positive. D. False, because the product of two negative real numbers is zero.

Solution Steps

The statement claims that the product of two negative real numbers is positive. We need to verify whether this is true or false.

The rule states that the product of two negative numbers is positive. For example, \( (-a) \times (-b) = ab \), where \( a \) and \( b \) are positive real numbers.

• Option A: False, because the product of two negative real numbers is negative.
  This is incorrect based on the rule mentioned in Step 2.

• Option B: True, because the product of two real numbers is always positive.
  This is incorrect because the product of two real numbers is not always positive (e.g., a positive and a negative number).

• Option C: True, because the product of two real numbers with the same sign is always positive.
  This is correct. The product of two negative numbers (same sign) is positive.

• Option D: False, because the product of two negative real numbers is zero.
  This is incorrect. The product of two negative numbers is not zero.

Final Answer