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Prove or Disprove: for All Real Numbers X And y,xy=xyy , \lfloor x - y \rfloor = \lfloor x \rfloor - \lfloor y \rfloor \text {. }

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Prove or disprove: For all real numbers x and y,xy=xyy , \lfloor x - y \rfloor = \lfloor x \rfloor - \lfloor y \rfloor \text {. }


Definitions:

Yerkes-Dodson Law

A theory that suggests there is an optimal level of arousal for the best performance on any task; too little or too much arousal can decrease performance.

REM

Rapid Eye Movement, a phase of sleep characterized by fast and random movement of the eyes, associated with dreaming.

NREM

Non-Rapid Eye Movement sleep, which is characterized by slower brain waves and serves as a period of rest and recovery for the body.

REM Sleep

A phase of sleep characterized by rapid eye movement, during which dreaming frequently occurs and the body undergoes increased brain activity.

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