Final answer:
The statement (x + y) = |x| + |y| is false because the sum of two integers is not always equal to the sum of their absolute values, especially when the integers have opposite signs.
Step-by-step explanation:
The statement that for any two integers x and y, (x + y) = |x| + |y| is false. The equation can be true or false depending on the signs of the integers x and y. The absolute value function, represented by |x|, always gives a non-negative result. Therefore, the sum of the absolute values |x| and |y| will be either equal to or greater than the sum (x + y) depending on the signs of x and y.
When x and y have the same sign (both positive or both negative), then (x + y) = |x| + |y| is true. However, if x and y have opposite signs, this equation is false. For example, if x = -2 and y = 3, then (x + y) = -2 + 3 = 1, but |x| + |y| = |-2| + |3| = 2 + 3 = 5.