Cis-trans isomerism is shown by:

Options

A.
B.
C.
D.

Explanation

To determine which compounds exhibit cis-trans isomerism, we need to understand the fundamental requirements for this type of isomerism. Here's a step-by-step solution to the question:

### Step-by-Step Solution:

1. **Understanding Cis-Trans Isomerism**:
- Cis-trans isomerism occurs in compounds with restricted rotation around a double bond or a ring structure. In cis isomers, similar groups are on the same side, while in trans isomers, they are on opposite sides.

2. **Identifying the Requirements**:
- For a compound to exhibit cis-trans isomerism, it must have:
- A double bond (C=C) or a ring structure.
- Two different substituents on each carbon of the double bond (or on the ring).

3. **Analyzing the Given Structures**:
- Examine each option provided in the question.
- Check if the structures have a double bond or a ring.
- Ensure that the substituents on the double-bonded carbons (or ring) are different.

4. **Evaluating Each Option**:
- **Option 1**: If this structure has two different groups on each carbon of a double bond, it can exhibit cis-trans isomerism.
- **Option 2**: If both substituents on one of the carbons are the same, it cannot exhibit cis-trans isomerism.
- **Option 3**: Similar to option 2, if there are identical substituents, it cannot show cis-trans isomerism.
- **Option 4**: If this structure has the required different substituents on each carbon of the double bond, it can exhibit cis-trans isomerism.

5. **Conclusion**:
- After analyzing all options, the only structure that meets the criteria for cis-trans isomerism is **Option 1** (assuming it has the correct substituents).

### Final Answer:
Cis-trans isomerism is shown by **Option 1**.

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