Numbers under 100 with three different prime factors are 30, 42, 66, 70 and 78.
Numbers under 100 with three different prime factors, at least one of which has multiplicity > 1 are 8, 12, 18, 20, 27, 28, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98 and 99.
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They are:
8, 12, 18, 20, 27,
28, 30, 42, 44, 45,
50, 52, 63, 66, 68,
70, 75, 76, 78, 92,
98, 99.
There are some that have more than 3 - which means that they do have 3.
[That last part is like the old riddle: how many months have 28 days - and the answer is all of them. Eleven have more than 28, but they do have 28.]
There are 4 prime numbers under ten.
30, 42, 66, 70 and 78.
There are 15 prime numbers less than 50.
By definition, a product of two primes has atwo factors (other than 1 and itself) and so it cannot be prime. So the set is not closed.
No.