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Did you know that a cockroach does not have a brain? Toughness vs weakness a rat can easily beat a cockroach in a battle so a rat definitely wins this fight. Weapon vs weapon a rat uses its teeth to crunch through Cockroaches and a cockroach uses its teeth at the front of its head to defend it from getting hurt habitat and habitat a rat lives wherever food is left behind it will set up home buying a house or buy an empty building with heaps of food if behind on the ground a  cockroaches habitat is in Little cracks inside Caves they like fitting their bodies inside tiny places. Who do you think will win before you think it's a rat remember a cockroach does not have a brain and can fit inside tiny gets gaps inside cave’s where a rat can not fit.