[A]: The Lac operon is an example of induc- ible system.
[R]: When Lactose, the inducer is present in the medium, it binds to the repressor making it ineffective.

Options

A. If both A and 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 and R is false
D. If both A and R are false

Answer

### Step-by-Step Solution:

1. **Understanding the Lac Operon**: The lac operon is a genetic system found in E. coli that regulates the metabolism of lactose. It is an example of an inducible system, meaning it can be activated in the presence of a specific substance—in this case, lactose.

2. **Components of the Lac Operon**: The lac operon consists of several key components:
- **Regulator Gene (I)**: Produces a repressor protein.
- **Promoter (P)**: Site where RNA polymerase binds to initiate transcription.
- **Operator (O)**: The site where the repressor binds.
- **Structural Genes (Z, Y, A)**: These genes code for enzymes that are involved in lactose metabolism:
- **Z**: Codes for beta-galactosidase, which breaks down lactose into glucose and galactose.
- **Y**: Codes for lac permease, which helps in the transport of lactose into the cell.
- **A**: Codes for transacetylase, an enzyme with a less clear function in lactose metabolism.

3. **Role of the Repressor**: In the absence of lactose, the repressor protein binds to the operator, preventing transcription of the structural genes. This keeps the lac operon in the "off" position.

4. **Induction by Lactose**: When lactose is present in the medium, it acts as an inducer. Lactose binds to the repressor protein, causing a conformational change that makes the repressor ineffective. As a result, the repressor can no longer bind to the operator.

5. **Activation of the Lac Operon**: With the repressor no longer bound to the operator, RNA polymerase can bind to the promoter and initiate transcription of the structural genes (Z, Y, A). This leads to the production of the enzymes necessary for lactose metabolism.

6. **Feedback Mechanism**: Once the lactose is consumed, there is no longer an inducer present. The repressor can again bind to the operator, turning the lac operon back "off."

7. **Conclusion**: Both statements in the question are true. The lac operon is indeed an example of an inducible system, and the reason provided accurately explains how lactose binds to the repressor, making it ineffective.

### Final Answer:
Both the assertion [A] and the reason [R] are true, and the reason [R] correctly explains the assertion [A].

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