Which of the following statement regarding `1,2`- dimethylcyclopropane (I) and `1,2`- dimethyl cyclobutane (II) are wrong

Options

A. Both of them show three stereoisomers.
B. The cis form of both is optically inactive (meso) and the trans form the both has a pair of enantiomers.
C. The cis form of both has a pair of enantiomers and the trans form of both is optically inactive (meso).
D. The meso form of both is optically inactive due to the presence of the centre of symmetry.

Answer

To determine which statements regarding `1,2`-dimethylcyclopropane (I) and `1,2`-dimethylcyclobutane (II) are wrong, we need to analyze the stereoisomers of both compounds.

### Step 1: Analyze 1,2-dimethylcyclopropane

1. **Draw the structure**:
- The structure of `1,2`-dimethylcyclopropane has two methyl groups attached to the first and second carbon of a cyclopropane ring.

2. **Identify stereoisomers**:
- **Cis form**: Both methyl groups are on the same side. This form has a plane of symmetry, making it a meso compound and optically inactive.
- **Trans form**: One methyl group is above the plane and the other is below. This form does not have a plane of symmetry, leading to two enantiomers (optically active).

3. **Count stereoisomers**:
- Total stereoisomers for `1,2`-dimethylcyclopropane: 3 (1 meso + 2 enantiomers).

### Step 2: Analyze 1,2-dimethylcyclobutane

1. **Draw the structure**:
- The structure of `1,2`-dimethylcyclobutane has two methyl groups on the first and second carbon of a cyclobutane ring.

2. **Identify stereoisomers**:
- **Cis form**: Both methyl groups are on the same side. This form also has a plane of symmetry, making it a meso compound and optically inactive.
- **Trans form**: One methyl group is above the plane and the other is below. This form does not have a plane of symmetry, leading to two enantiomers (optically active).

3. **Count stereoisomers**:
- Total stereoisomers for `1,2`-dimethylcyclobutane: 3 (1 meso + 2 enantiomers).

### Step 3: Evaluate the statements

1. **Statement 1**: Both of them show 3 stereoisomers.
- **Evaluation**: Correct. Both compounds have 3 stereoisomers.

2. **Statement 2**: The cis form of both is optically inactive meso and the trans form has a pair of enantiomers.
- **Evaluation**: Correct. The cis forms are meso and optically inactive, while the trans forms are enantiomers.

3. **Statement 3**: The cis form of both has a pair of enantiomers.
- **Evaluation**: Incorrect. The cis forms are meso compounds and do not have enantiomers.

4. **Statement 4**: The meso form is optically inactive due to the presence of a center of symmetry.
- **Evaluation**: Incorrect. The meso form is optically inactive due to the presence of a plane of symmetry, not a center of symmetry.

### Conclusion

The wrong statements are:
- Statement 3: "The cis form of both has a pair of enantiomers."
- Statement 4: "The meso form is optically inactive due to the presence of a center of symmetry."