Entropy change for an irreversible process taking system and surrounding together is

For an isolated system the entropy change is always goes on increasing (second law of thermodynamics). Given, the system and surroundings are taken together that means the resulting system will be an isolated system and in that isolated system if the interactions between the system and surroundings are irreversible we the entropy change will be greater than zero and if the interactions are reversible the entropy change will be equal to zero.
$$\Delta {S_{isolated\,\,system}} \geqslant 0$$