Both the proposition and its converse (“If n is not a multiple of 3, then n and n + 3 have no factors in common”) are true, since common prime factors must divide (n + 3) – n = 3.
Ganita Manjari part 2 chapter 9.1 solutions
Class 9 Ganita Manjari Part 2 chapter 9 Page 6 Question Answer
Both the proposition and its converse (“If n is not a multiple of 3, then n and n + 3 have no factors in common”) are true. Any common factor of n and n + 3 must divide their difference, (n + 3) – n = 3. Hence, 3 is the only possible common prime divisor. Thus, they share common factors if and only if n is a multiple of 3.
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