Question

"An integer is negative if and only if it is less than zero."

If this statement is true, then which of the following statements must also be true?

A. An integer is negative if and only if it is not less than zero.
B. An integer is not negative if and only if it is less than zero.
C. An integer is not negative if and only if it is not less than zero.
D. An integer is less than zero if and only if it is not negative.

Answer 1

B is the answer cause I just need points

Answer 2

• An integer is not negative if and only if it is not less than zero.

Explanation:

Observing each statement individually:

• An integer is negative if and only if it is not less than zero

A number that is NOT less than 0 is greater than zero. Negative numbers are less than 0, so this is clearly incorrect.

• An integer is not negative if and only if it is less than zero.

A number that is NOT negative is positive. Positive integers are integers greater than zero, so this is also incorrect.

• An integer is not negative if and only if it is not less than zero.

A number that is NOT negative is positive. A number that is NOT less than zero is greater than zero, or positive. This statement is correct.

• An integer is less than zero if and only if it is not negative.

A number that is less than zero is negative, and this statement claims that a number less is only less than zero if it is NOT negative. This is incorrect.