`beta-`Hydroxy propanoic acid on heating gives acrylic acid.
Acrylic acid exists in two diastereomers.

Options

A. If both `(A)` are `( R)` are true and `( R)` is the correct explanation of `(A)`.
B. If both `(A)` and `( R)` are true but `( R)` is not the correct explanation of `(A)`.
C. If `(A)` is true but `( R)` is false.
D. If `(A)` is false but `( R)` is true.

Explanation

To solve the question, we need to analyze the reaction of β-hydroxy propanoic acid and understand the properties of acrylic acid.

### Step-by-step Solution:

1. **Identify β-Hydroxy Propanoic Acid**:
- β-Hydroxy propanoic acid is a carboxylic acid with a hydroxyl group (-OH) on the β-carbon (the second carbon in the chain). Its structure can be represented as:
\[ \text{HO-CH(CH_3)-COOH} \]
- This compound has the following structure:
\[ \text{CH}_3-\text{CH(OH)}-\text{COOH} \]

2. **Heating β-Hydroxy Propanoic Acid**:
- When β-hydroxy propanoic acid is heated, it undergoes dehydration (loss of water). The hydroxyl group (-OH) from the β-carbon and a hydrogen atom from the α-carbon are removed, resulting in the formation of a double bond between the α and β carbons.
- The reaction can be summarized as:
\[ \text{HO-CH(CH_3)-COOH} \xrightarrow{\text{heat}} \text{CH}_2=\text{CH-COOH} + \text{H}_2\text{O} \]
- The product formed is acrylic acid (prop-2-enoic acid).

3. **Structure of Acrylic Acid**:
- The structure of acrylic acid is:
\[ \text{CH}_2=\text{CH-COOH} \]
- This compound has a double bond between the first and second carbon atoms.

4. **Diastereomers of Acrylic Acid**:
- Acrylic acid can exist as two diastereomers due to the presence of the double bond and the carboxylic acid group. However, since both substituents on the double bond (the hydrogen and the carboxylic acid group) are not identical, it does not exhibit diastereomerism in the traditional sense.
- The two possible configurations (E and Z) around the double bond can be considered, but they do not lead to distinct diastereomers since they do not have different physical properties.

5. **Conclusion**:
- The assertion that β-hydroxy propanoic acid gives acrylic acid upon heating is true.
- The reason stating that acrylic acid exists in two diastereomers is false because it does not exhibit such isomerism.

### Final Answer:
- The correct option is **C**: Assertion is true, but the reason is false.