[7 points] Dene a relation I on N as follows: a E b if and only if a has exactly the same set of prime factors as b. (For example, 12 E 18 because...

[7 points] Dene a relation  on N as follows:

a  b if and only if a has exactly the same set of prime factors as b.

(For example, 12  18 because 12 = 22 3 and 18 = 2  32, but 12 6 30 because

30 = 235, so 30 has a prime factor which is not a factor of 12.) Show that

is an equivalence relation on N.