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I know how suction cups work (or I think I do):

You push on the suction cup, pushing all the air out, which creates a low pressure. The cup is held in place because of the higher pressure of the atmosphere is pushing against the cup.

What gas law would this be?

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Tiny objection to Sammy's answer: it's pretty trivially the ideal gas equation of state. True, as Sammy says, "high force from atmospheric pressure" versus "little force from partial vacuum". But note that the suction cup always has to lift up from the table at least a little bit in order to create a non-zero volume containing (pretty much) zero moles of gas, whereby we now have $PV=nRT$ with $n=0,V>0$ so that necessarily $P=0$. You've got to put that equation "into play", so to speak, by creating a $V>0$ volume when the suction cup lifts slightly off the table.

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This does not happen as a result of any gas law. It happens because there is a surprisingly high force from the atmosphere pressing down on the suction cups, and comparatively little force pressing up from the table and partial vacuum below.

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