13 Let X12 1 2 3 4 5 6 7 8 910 11 12 and let R be the equiv

13. Let X12 = {1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12} and let R be the equivalence relation on X12 given by aRb . a and b have the same set of prime divisors The number of distinct equivalence classes is

Solution

SET OF PRIME DIVISORS FOR X12 ARE ..

[1]=[ NONE ] ... NOTE THAT 1 IS NOT CONSIDERED AS A PRIME NUMBER

[2] = [ 2] ........[3] = [3]........[4 ] = [ 2] ........[5] = [ 5]........[6] = [ 2 , 3 ] ......[ 7 ] = [ 7 ]....[8] = [ 2 , 4 ]

[ 9 ] = [ 3 ] .... [10 ] = [ 2 , 5 ] ......[ 11 ] = [ 11 ]....[12] = [ 2 , 3 ]

A R B IF A & B HAVE SAME SET OF PRIME DIVISORS ...IT MEANS IDENTICAL SET OF PRIME DIVISORS ..

WE HAVE ONLY 2 SUCH NUMBERS [ 6 ] & [ 12 ] ...SO ...6 R 12 AND 12 R 6 ...THERE ARE NO OTHER PAIR OF ELEMENTS WITH IDENTICAL SET OF PRIME DIVISORS ..

SO WE HAVE IN ALL ...10 DISTINCT SETS ...IS THIS WHAT YOU ARE LOOKING FOR ? ...

IT IS NOT VERY CLEAR WHAT YOU ARE LOOKING FOR