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In 2265, after hearing Hikaru Sulu's mathematical estimation of the rate Gary Mitchell's powers would increase by, Spock told James T. Kirk that in a month, Mitchell would have as much in common with the rest of the crew of the USS Enterprise as that same crew now would have with a ship of white mice.(TOS: "Where No Man Has Gone Before")
Cats are traditionally known to chase mice. As of 2370, Data's cat Spot had never encountered a mouse or any other form of rodent, which once left Data at a loss to explain what the cat was dreaming about. (TNG: "Phantasms")
The cat-and-mouse relationship eventually lent itself to the phrase "cat-and-mouse game", when one individual or group persistently chases another. (TOS: "Friday's Child", "The Squire of Gothos"; TAS: "Once Upon a Planet"; VOY: "Equinox, Part II")