Question

state two statement of second law of thermodynamics also prove that both are equuivalent

Answer 1

The "sole effect" in the two statements is a wrong requirement that converts them into true but trivial propositions, having nothing to do with the second law of thermodynamics. Consider the following scenario. An operator carries out heat and work exchanges between the system and the environment (which is the only heat reservoir). If, at the end of the cycle, the system is in its initial state, a weight is lifted in the environment, and an equivalent amount of heat is missing in the environment, the second law is obviously violated. Yet, according to the Kelvin statement you refer to, the second law is not violated - the "sole effect" requirement is not obeyed. Apart from the lifted weight and the missing heat, which are allowed by the "sole effect" requirement, there are also unallowed but unavoidable changes in the operator.

The "sole effect" requirement is much more pernicious in the Clausius case - the statement becomes equivalent to

Heat cannot move SPONTANEOUSLY from cold to hot

which is true but trivial and has nothing to do with the second law.