The proposition is true with divisors 1, p, q and pq. Its converse (“If n has exactly 4 divisors, then it is a product of two unequal prime numbers”) is false; n = 8 = 2³ has 4 divisors.
Class 9 Maths Ganita Manjari Part 2 All Chapter Solutions
Class 9 Maths Ganita Manjari Part 2 Chapter 9 Question Answer
The proposition is true because n = pq (where p ≠ q are primes) has divisors 1, p, q and pq. However, the converse—”If n has exactly 4 divisors, then it is a product of two unequal prime numbers”—is false. As a counterexample, n = 8 = 2³ has exactly 4 divisors (1, 2, 4, 8), but 8 is a prime cube, not a product of two unequal primes.
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