Assertion: In `C_(4)` plants, the bundle sheath cells are rich in an enzyme phosphoate carboxylase-oxygenase (PEP case). Reason: In `C_(4)`,the mesophyll cells are rich in an enzyme ribulose carboxylase-oxygenase(RuBisCo)

Explanation

### Step-by-Step Solution:

1. **Understanding C4 Plants**: C4 plants have a unique photosynthetic pathway that involves two types of cells: mesophyll cells and bundle sheath cells.

2. **Assertion Analysis**: The assertion states that in C4 plants, the bundle sheath cells are rich in the enzyme phosphoenol carboxylase-oxygenase (PEP case). This is incorrect. Bundle sheath cells primarily contain the enzyme ribulose carboxylase-oxygenase (RuBisCO), which is crucial for the Calvin cycle.

3. **Reason Analysis**: The reason states that in C4 plants, the mesophyll cells are rich in the enzyme ribulose carboxylase-oxygenase (RuBisCO). This is also incorrect. Mesophyll cells are rich in phosphoenolpyruvate carboxylase (PEP case), which is responsible for the initial fixation of CO2.

4. **Conclusion**: Since both the assertion and the reason are incorrect, the correct conclusion is that both statements are false.

5. **Final Answer**: Therefore, the answer is D: Both assertion and reason are false.