A: Optical communication system is more economical than other system of communications.
R: The information carrying capacity of a communication system is directly proportional to its band width.

Answer

To analyze the given statements and determine their validity, we can follow these steps:

### Step 1: Understand the Assertion (A)
The assertion states that "Optical communication system is more economical than other systems of communications."
- **Explanation**: Optical communication systems, particularly those using optical fibers, tend to be more cost-effective in the long run due to lower operational costs, higher data transmission rates, and reduced need for maintenance compared to traditional systems like radio or microwave communication.

### Step 2: Understand the Reason (R)
The reason states that "The information carrying capacity of a communication system is directly proportional to its bandwidth."
- **Explanation**: This statement is based on the principle that a higher bandwidth allows for more data to be transmitted simultaneously. In communication systems, bandwidth is a critical factor that determines the amount of information that can be sent over a channel.

### Step 3: Analyze the Relationship Between A and R
Now, we need to evaluate if the reason (R) supports the assertion (A).
- **Explanation**: Since optical communication systems utilize a wide bandwidth, they can carry more information than systems with narrower bandwidths. This increased capacity contributes to the overall economy of the system, as it allows for more efficient data transmission and reduces the need for additional infrastructure.

### Step 4: Conclusion
Both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion. Therefore, the assertion is justified by the reason provided.

### Final Answer
Both the assertion and reason are true, and the reason correctly explains the assertion.

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