In this paragraph, some statements are given based on isomerism. Read the following statements given for every question and provide the answer.
Which of the following structrues of a cyclic alkene with the lowest number of `C` atoms shows both geometrical and optical isomerism?

Options

A.
B.
C. Both
D. None

Answer

To solve the question regarding which cyclic alkene structure shows both geometrical and optical isomerism with the lowest number of carbon atoms, we can follow these steps:

### Step 1: Identify the Structures
We need to analyze the given cyclic compounds A and B. We should focus on their carbon atom counts and their potential for geometrical and optical isomerism.

### Step 2: Count the Carbon Atoms
- For **Compound A**:
- The structure includes a cyclopropane ring with additional substituents.
- Count the carbon atoms: 1 (from the ring) + 1 (from the methyl group) + 4 (from the ethynyl group) = **6 carbon atoms**.

- For **Compound B**:
- The structure also includes a cyclic component with substituents.
- Count the carbon atoms: 1 (from the ring) + 6 (from the substituents) = **7 carbon atoms**.

### Step 3: Determine Geometrical Isomerism
- **Geometrical Isomerism**: This occurs in compounds with restricted rotation around a double bond or in cyclic structures.
- **Compound A** can exist in both cis and trans forms due to the presence of substituents on the ring, which allows for geometrical isomerism.
- **Compound B** also shows geometrical isomerism, but we need to check the optical isomerism next.

### Step 4: Determine Optical Isomerism
- **Optical Isomerism**: This occurs when a compound lacks a plane of symmetry or a center of symmetry, making it chiral.
- For **Compound A**: The cis form of Compound A does not have a plane of symmetry or a center of symmetry, making it optically active. The trans form also lacks symmetry, thus it is also optically active.
- For **Compound B**: The cis form has a plane of symmetry, making it optically inactive, while the trans form is optically active. However, since we are looking for a compound that shows both types of isomerism, Compound B does not satisfy this requirement.

### Step 5: Conclusion
Since Compound A has 6 carbon atoms and shows both geometrical and optical isomerism, it is the correct answer. Compound B, while showing geometrical isomerism, does not show optical isomerism in both forms.

### Final Answer
The structure of a cyclic alkene with the lowest number of carbon atoms that shows both geometrical and optical isomerism is **Compound A**.

---