For an irreversible process, the value of $\left[\Delta {\mathrm{S}}_{\text{(system) }}+\Delta {\mathrm{S}}_{\text{(surroundings) }}\right]$ is

 In case of reversible process, if entropy of system increases by some amount, then entropy of surrounding decrease by the same amount and total entropy change is zero. In case of irreversible process, total entropy change is always greater than zero.

So, $\left[\Delta {\mathrm{S}}_{\text{(system) }}+\Delta {\mathrm{S}}_{\text{(surroundings) }}\right]$>0

Therefore, option A is correct.