Consider an equivalence relation R on the positive integers A = {2, 3, 4, 5, 6, 7, .. 22} defined as mRn if the largest prime divisor of 'm' is the same as the largest prime divisor of 'n' The number of equivalence classes of R is ________.

8

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Solution

The correct option is A 8
"mRn" (largest prime divisor of m = largest prime divisor of 'n')
So, equivalence classes are
1. 2 R {2, 4, 8, 16 }
2. 3 R {3, 6, 9, 12, 18, 21}
3. 5 R { 5, 10, 15, 20}
4. 7 R {7, 14, 21}
5. 11 R {11, 22}
6. 13 R {13}
7. 17 R{17}
8. 19 R{19}
Number of equivalence classes are 8.

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Consider an equivalence relation R on the positive integers A = {2, 3, 4, 5, 6, 7, .. 22} defined as mRn if the largest prime divisor of 'm' is the same as the largest prime divisor of 'n' The number of equivalence classes of R is ________. 8

Consider an equivalence relation R on the positive integers A = {2, 3, 4, 5, 6, 7, .. 22} defined as mRn if the largest prime divisor of 'm' is the same as the largest prime divisor of 'n' The number of equivalence classes of R is ________.

8