Assertion (A): The cis form of
`(CH_(3)-underset(Cl)underset(|)(CH)-CH=CH-underset(Cl)underset(|)(CH)-CH_(3))`
exist in three-diastereomers.
Reason (R ): One form is optically inactive due to the presence of centre of symmetry.

Options

A. If both (A) and (R ) are true and (R ) is the correct explanation for (A).
B. If both (A) and (R ) are true and (R ) is not the true explanation for (A)
C. If (A) is true, but (R ) is false.
D. If both (A) and (R ) are false

Explanation

To solve the question, we need to analyze the assertion and reason provided.

### Step 1: Understanding the Assertion
The assertion states that the cis form of the compound `(CH₃-Cl-CH=CH-Cl-CH₃)` exists in three diastereomers.

1. **Identify the structure**: The compound has a double bond between two carbon atoms, and each of these carbon atoms is attached to different groups (Cl, CH₃, and H).
2. **Cis form**: The cis form means that the two Cl atoms are on the same side of the double bond.
3. **Chirality**: Each of the two carbons involved in the double bond is chiral because they are attached to four different groups.

### Step 2: Counting Diastereomers
To determine the number of diastereomers:
1. **Chiral centers**: There are two chiral centers in the compound.
2. **Formula for diastereomers**: The number of diastereomers can be calculated using the formula \(2^n\), where \(n\) is the number of chiral centers. However, we need to account for the fact that some of these may be meso compounds (optically inactive).
3. **Meso compounds**: In this case, the presence of a plane of symmetry in one of the configurations leads to the formation of a meso compound.

### Step 3: Conclusion on Assertion
- **Total diastereomers**: After considering the chiral centers and meso form, we find that the total number of diastereomers is indeed three (2 optical isomers + 1 meso compound).
- Therefore, the assertion is **true**.

### Step 4: Understanding the Reason
The reason states that one form is optically inactive due to the presence of a center of symmetry.

1. **Optical inactivity**: The meso form is optically inactive due to its symmetry. However, it is important to note that this is due to a **plane of symmetry**, not a center of symmetry.
2. **Center of symmetry**: A center of symmetry is a point in the molecule where for every atom, there is an equivalent atom at an equal distance on the opposite side. In this case, the compound does not have a center of symmetry.

### Step 5: Conclusion on Reason
- Since the reason incorrectly attributes the optical inactivity to a center of symmetry instead of a plane of symmetry, the reason is **false**.

### Final Conclusion
- The assertion is true, and the reason is false. Therefore, the correct answer is that the assertion is true, and the reason is false.