True or False: $(10$ pts$)$

a$.$ A process cannot occur unless it satisfies both the first and the second laws of thermodynamics.

b$.$ The COP of a refrigerator cannot be less than $1.$

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c$.$ No heat engine can convert all the heat it receives to useful work. $$

d$.$ The entropy change between two specified states depends on the path followed during a process. $$

e$.$ No entropy is generated during the complete combustion of a fuel in an adiabatic test chamber. $$