सूची I को सूची II से सुमेलित कीजिए तथा सही उत्तर चुनिए: सूची I (तर्क में नियम) P. मोड्स पोनेंस (Modus Ponens) Q. मोड्स टोलेंस (Modus Tollens) R. वियोजनात्मक न्यायवाक्य (Disjunctive Syllogism) S. काल्पनिक न्यायवाक्य (Hypothetical Syllogism) सूची II (प्रतीकात्मक निरूपण)1. ((p → q) ∧ (q → r)) → (p → r)2. (¬p ∧ (p ∨ q)) → q3. (p ∧ (p → q)) → q4. (¬q ∧ (p → q)) → ¬p

Given below are two statements, one labelled as Assertion (a) and the other labelled as Reason (r). Read the statements and choose the correct answer from the code given below: Assertion (a): A department contains 13 professors. Then two of the professors were born in the same month. Reason (r): The Pigeonhole Principle states that if there are more 'pigeons' than 'pigeonholes', there must be at least one pigeonhole with more than one pigeon.

What is the value of the term a3 for the recurrence relation an = 2an-1 + 1, given the initial condition a0 = 1?