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equivalence classes are with respect to equivalence relation. Given that relation R as, mRn iff m,n are have largest prime divisor common.

10 prime divisors are 2,5. so largest prime divisor of 10 is 5. so 5R10 but not 2R10.

prime numbers will not combine with ither prime numbers due to no two prime numbers doesn't have common divisors.

SO, 2,3,5,7,11,13,17,19 will create different equivalence classes.

remaining number must comined with any prime number. i mean 15 have 2,3,5 common divisors. So 15 should relate to 5 in R. therefore it will go into equivalence classe of 5.

10 prime divisors are 2,5. so largest prime divisor of 10 is 5. so 5R10 but not 2R10.

prime numbers will not combine with ither prime numbers due to no two prime numbers doesn't have common divisors.

SO, 2,3,5,7,11,13,17,19 will create different equivalence classes.

remaining number must comined with any prime number. i mean 15 have 2,3,5 common divisors. So 15 should relate to 5 in R. therefore it will go into equivalence classe of 5.

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