If x and y are both negative integers, the value of x - y must also be a negative integer. — Armed Services Vocational Aptitude Battery (ASVAB)

If $x$ and $y$ are both negative integers, the value of $x - y$ must also be a negative integer.

Answer: Answer

False

The statement is false. When evaluating

x - y

with negative integers, the operation simplifies to adding a positive number. If the magnitude of

y

is larger than the magnitude of

x

, the result is positive. For instance, if

x = -1

and

y = -5

, then

-1 - (-5) = 4

Analyze the expression

x - y

given that both variables represent negative integers.

Since

y

is negative, subtracting

y

is identical to adding the absolute value of

y

. The expression becomes

x + |y|

Understanding how double negatives simplify is essential for evaluating integer properties.

Test the statement using a counterexample where

y

is further left on the number line than

x

Assume

x = -3

and

y = -10

. Substitute these integers into the original expression:

-3 - (-10)

A universally phrased statement containing the word 'must' can be entirely disproven with just a single counterexample.

Evaluate the chosen counterexample.

-3 - (-10) = -3 + 10 = 7

. Because

7

is a positive integer, the expression does not always yield a negative result.

The positive outcome proves the initial statement is definitively false.

Integer Subtraction and Sign Rules

Estimated Time:35s

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