Question

Which statements are not true and true?

statement 1: the sum of two negative integers is positive

Statement 2: the product of two negative integers is positive

Statement 3: the difference of two negative integers is positive

Statement 4: the quotient of two negative integers is positive


For both statements that are not true at all, provide one counter example for each statement that proves the statement can be false.

Answer 1

Answer: Statements 1, 3, and 4 are not true. The sum, difference, and quotient of two negative integers can be positive, negative, or zero, depending on the values of the two integers. For example, the sum of -5 and -7 is -12, which is a negative number. The difference of -5 and -7 is 2, which is a positive number. The quotient of -5 and -7 is -0.7142857142857143, which is a negative number.

Only statement 2 is true. The product of two negative integers is always a positive number. For example, the product of -5 and -7 is 35, which is a positive number. This is because the two negative signs "cancel out" when multiplying two numbers, resulting in a positive product.