Which of the following statements are correct?

Options

A. Methyl cyclopropane and methyl cyclobutane do not show stereoismerism.
B. Both show stereoisomerism.
C. 1,2-Dimethyl cyclopropane shows stereoisomerism, but methyl cyclobutane does not.
D. 1,2-Dimethyl cyclopropane does not show stereoisomerism, but methyl cyclobutane shows.

Answer

To determine which statements are correct regarding methyl cyclopropane, methyl cyclobutane, and 1,2-dimethylcyclopropane, we will analyze each statement step by step.

### Step 1: Analyze Methyl Cyclopropane and Methyl Cyclobutane
- **Methyl Cyclopropane**: This is a cyclopropane ring with one hydrogen atom replaced by a methyl group. It is a monosubstituted cycloalkane.
- **Methyl Cyclobutane**: This is a cyclobutane ring with one hydrogen atom replaced by a methyl group. It is also a monosubstituted cycloalkane.

**Conclusion**: Both methyl cyclopropane and methyl cyclobutane are monosubstituted cycloalkanes and do not have chiral centers. Therefore, they cannot exhibit stereoisomerism (neither geometrical nor optical).

### Step 2: Evaluate the Statements
1. **Statement 1**: "Methyl cyclopropane and methyl cyclobutane do not show stereoisomerism."
- **Correct**: As established, both compounds do not show stereoisomerism.

2. **Statement 2**: "Both show stereoisomerism."
- **Incorrect**: This contradicts our conclusion from Step 1.

3. **Statement 3**: "1,2-dimethylcyclopropane shows stereoisomerism but methyl cyclobutane does not."
- **Correct**: 1,2-dimethylcyclopropane can exhibit stereoisomerism due to the presence of two methyl groups that can be arranged in cis and trans forms. Methyl cyclobutane, as previously established, does not show stereoisomerism.

4. **Statement 4**: "1,2-dimethylcyclopropane does not show stereoisomerism, but methyl cyclobutane shows."
- **Incorrect**: This statement is false because 1,2-dimethylcyclopropane does show stereoisomerism.

### Final Conclusion
The correct statements are:
- **Statement 1**: Methyl cyclopropane and methyl cyclobutane do not show stereoisomerism.
- **Statement 3**: 1,2-dimethylcyclopropane shows stereoisomerism but methyl cyclobutane does not.

### Summary of Correct Statements
- **Correct Statements**: 1 and 3.