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Question:

would a vacuum cleaner pick up dust from a rug on the moon?

the pump in a vacuum cleaner is merely a high-speed fan.its a physics Q

Answer:

Maybe if it was a Hoover. The questions get sillier.
No. In a canister vacuum the fan reduces the pressure in a chamber containing a filter. If the pressure in the chamber is already zero it cannot be reduced.
No. Fluids move from high pressure to low pressure. Vacuum cleaners work by making a lower pressure system inside the vacuum cleaner, but because you cannot make pressure lower than what it is in vacuum (space), so the vacuum cleaners cannot pick anything up, because the pressure is higher than the vacuum of space.
No, their can be no suction without a fluid to pull and push around.

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