people usually use logic in math and math in logic
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It can be. It can rely on logic, and logic is related to math. In making arguments, they can use a lot of mathematical elements, like establishing numbers to prove the argument they are making.
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Yes, because logic and deduction are part of math.
It develops the power to apply logic and logic in an integral part of mathematics.
Rocks are related to math because of geology and in geology you use math.