A solution of A and B shows positive deviation from Raoult's law, which of the following statement is true for the solution
I. `Delta V_("mix") gt 0` II `Delta G_("mix") lt 0` III. `Delta H_("mix") gt 0` IV `Delta S_("mix") gt 0`

Options

A. I and III only
B. I, II and III only
C. I, II, III and IV
D. I, III and IV only

Explanation

To solve the question regarding the solution of A and B that shows positive deviation from Raoult's law, we will analyze each statement provided and determine which ones are true based on the properties of such a solution.

### Step-by-Step Solution:

1. **Understanding Positive Deviation from Raoult's Law**:
- A positive deviation from Raoult's law occurs when the vapor pressure of the solution is higher than expected. This happens when the interactions between the solute and solvent molecules are weaker than those between the solvent-solvent and solute-solute molecules.

2. **Analyzing the Statements**:
- **Statement I: `Delta V_(mix) > 0`**:
- In positive deviation, the volume of the mixture increases upon mixing due to the weaker interactions. Therefore, this statement is **true**.

- **Statement II: `Delta G_(mix) < 0`**:
- The change in Gibbs free energy (ΔG) for mixing is generally negative for spontaneous processes. However, in the case of positive deviation, ΔG can be positive or zero, but it is not guaranteed to be less than zero. Hence, this statement is **false**.

- **Statement III: `Delta H_(mix) > 0`**:
- Positive deviation is associated with endothermic mixing, meaning heat is absorbed during the process. Therefore, ΔH is greater than zero. This statement is **true**.

- **Statement IV: `Delta S_(mix) > 0`**:
- The entropy of the system increases when mixing occurs due to the increased disorder from the weaker interactions. Thus, ΔS is greater than zero. This statement is **true**.

3. **Conclusion**:
- The true statements are I, III, and IV. Therefore, the correct option is that statements I, III, and IV are true.

### Final Answer:
The correct statements are:
- I. `Delta V_(mix) > 0`
- III. `Delta H_(mix) > 0`
- IV. `Delta S_(mix) > 0`

Thus, the answer is that statements I, III, and IV are true.