Prove or disprove: For all positive real numbers x and y$\lceil x \cdot y \rceil \leq \lceil x \rceil \cdot \lceil y \rceil$

Question

Quizplus · Accepted Answer

The ceiling function rounds up to the nearest integer, so $\lceil x \cdot y \rceil$ rounds up the product of x and y to the nearest integer. $\lceil x \rceil \cdot \lceil y \rceil$ rounds up x and y to the nearest integers and then multiplies them, so it is always greater than or equal to $\lceil x \cdot y \rceil$.

Prove or Disprove: for All Positive Real Numbers X and Y