The two statements of the second law may not appear to have anything to do with one another, but in fact each one implies the other.
The top line shows yellow engines representing hypothetical engines violating each of the two statements of the second law. The second line shows that an engine which violates Kelvin's statement, together with a normal heat pump, violates Clausius's statement. A similar drawing can be used to show that an pump which violates Clausius's statement, together with a normal heat engine, violates Kelvin's statement. Hence the two statements--which seem quite different--are actually equivalent.