Which of the following relation is not correct?

Let us verify each relation:

Option A: $$\Delta H = \Delta U - P\Delta V$$

The correct relation between enthalpy change and internal energy change is:

$$\Delta H = \Delta U + P\Delta V$$

The given relation has a minus sign instead of a plus sign, making it incorrect.

Option B: $$\Delta U = q + W$$

This is the first law of thermodynamics, which states that the change in internal energy equals the heat added to the system plus the work done on the system. This relation is correct.

Option C: $$\Delta S_{sys} + \Delta S_{surr} \geq 0$$

This is the second law of thermodynamics, which states that the total entropy of the universe (system + surroundings) never decreases. This relation is correct.

Option D: $$\Delta G = \Delta H - T\Delta S$$

This is the Gibbs free energy equation (at constant temperature and pressure). This relation is correct.

Therefore, the relation that is not correct is Option A: $$\Delta H = \Delta U - P\Delta V$$.