Step 1: Understanding the Concept:
The question explores the definitions of lunar months in the Vedic tradition. A lunar month is generally defined as the period between two consecutive New Moons (Amanta) or Full Moons (Purnimanta).
Step 2: Detailed Explanation of Assertion (A):
In the older Vedic layers, months were categorized based on their celestial characteristics. 'Vidhoma' and 'Paitra' (Ancestral) are terms that describe cycles of the moon in relation to the sun and the nodes. These represent specific types of 'Maasas' or month-long observations used in the Vedic calendar (like the Vedanga Jyotisha or the Brahmanas). Assertion (A) is historically and textually correct as it identifies these as valid lunar month classifications.
Step 3: Detailed Explanation of Reason (R):
Reason (R) states the mathematical definition of a lunar month: \( 30 \text{ Tithis} = 1 \text{ Chandra Maasa} \). This is a foundational rule in Indian astronomy. One Tithi is the time taken for the Moon to gain 12 degrees on the Sun. Thirty such increments make 360 degrees, completing the cycle from one conjunction to the next. Thus, (R) is a correct statement of fact.
Step 4: Evaluating the Link:
While both statements are true, (R) does not explain why specific names like 'Vidhoma' are given to certain months. The names 'Vidhoma' or 'Paitra' come from the quality of the moon's light or its relation to rituals, not from the simple fact that a month has 30 tithis. Every lunar month has 30 tithis, but not every lunar month is called 'Vidhoma'. Therefore, the Reason is a general rule that does not provide a specific explanation for the technical names mentioned in the Assertion.
Step 5: Final Answer:
Both are correct statements, but (R) is not a specific explanation for (A).