The gynoecium is monocarpellary in the members of family Solanaceae.

Answer

To determine whether the statement "The gynoecium is monocarpellary in the members of family Solanaceae" is true or false, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Family**: The question refers to the Solanaceae family, which is commonly known as the nightshade family. This family includes many economically important plants such as tomatoes, potatoes, and eggplants.

2. **Understand Gynoecium Structure**: The gynoecium is the female reproductive part of a flower, consisting of one or more carpels. A monocarpellary gynoecium means that the flower has only one carpel, while a bicarpellary gynoecium means there are two carpels.

3. **Research the Gynoecium in Solanaceae**: In the Solanaceae family, the gynoecium is primarily characterized as bicarpellary. This means that most members of this family possess two carpels.

4. **Additional Characteristics**: The gynoecium in Solanaceae is also described as syncarpous, meaning that the carpels are fused together. It is typically bilocular (having two cavities) and may have a false septum due to the fusion of the carpels.

5. **Conclusion**: Since the statement claims that the gynoecium is monocarpellary, and we have established that it is actually bicarpellary, we conclude that the statement is false.

### Final Answer:
The statement "The gynoecium is monocarpellary in the members of family Solanaceae" is **false**.

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