Final answer:
The equation ceil(x + y) = ceil(x) + ceil(y) holds true for certain real numbers x and y only when both ceil(x) and ceil(y) are integers.
Step-by-step explanation:
The equation ceil(x + y) = ceil(x) + ceil(y) holds true for certain real numbers x and y. The equation compares the ceiling function, ceil(), which rounds a number up to the nearest integer, with the addition of x and y. To satisfy this equation, both ceil(x) and ceil(y) must be integers because the sum of two integers is always an integer. If x and y have decimal parts, their sum will have a decimal part as well, and the equation will not hold true.
For example, let's consider x = 2.5 and y = 3.3. ceil(x) is 3 and ceil(y) is 4. The sum of ceil(x) and ceil(y) is 7. On the other hand, ceil(x + y) is ceil(5.8) which is 6. Since ceil(x + y) is not equal to ceil(x) + ceil(y), these values of x and y do not satisfy the equation.
Therefore, the equation ceil(x + y) = ceil(x) + ceil(y) is true for real numbers x and y only when both ceil(x) and ceil(y) are integers.