Okay, let's see. The question is asking for the number of elements in the intersection of two sets. The first set is all prime numbers less than 30, and the second set is all odd numbers greater than zero. So, I need to find how many numbers are both prime and odd, right?

First, let me recall what prime numbers are. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. The first few primes are 2, 3, 5, 7, 11, and so on. But wait, 2 is the only even prime number. All other primes are odd because any even number greater than 2 can be divided by 2, so they're not prime.

So, if we're looking for primes less than 30, we can list them out. Let me do that. Starting from 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Let me check if these are all primes under 30. 2 is prime, 3 is prime, 5 is prime, 7 is prime. Then 11, 13, 17, 19, 23, 29. 29 is the last one before 30. So that's 10 prime numbers in total.

Now, the second set is all odd numbers greater than zero. Well, odd numbers are numbers not divisible by 2. So starting from 1, 3, 5, 7, 9, ..., up to, well, any odd number. But since we're intersecting with the primes less than 30, we can limit our consideration to odd numbers less than 30 as well, except for 1, which is odd but not prime.

But wait, the intersection of primes (which are mostly odd) and odd numbers would just be the primes themselves, except for 2. But since 2 is even and the other primes are odd, the intersection would exclude 2. Let me confirm that. The intersection would be all numbers that are both prime and odd. Since 2 is the only even prime, the intersection would be all primes less than 30 except 2. So that would be 9 elements? Wait, but let's check.

Wait, the primes less than 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. So that's 10 primes. If we remove 2, which is the only even prime, then the intersection with odd numbers would be 9 primes. But hold on, the set of odd numbers greater than zero includes all odd numbers, but the primes less than 30 include both 2 and the odd primes. So the intersection would be the odd primes less than 30.

But 2 is not odd, so it's not in the intersection. Therefore, the intersection would be 3, 5, 7, 11, 13, 17, 19, 23, 29. That's 9 numbers. So the answer should be 9.

Wait, but let me double-check. Let's list all primes less than 30 again: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. That's 10 primes. The odd numbers greater than zero are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, etc. But since we're only considering primes less than 30, the intersection would be the primes that are odd. So excluding 2, which is even, the rest are odd. So 10 primes minus 1 (the number 2) gives 9. Therefore, the intersection has 9 elements.

But wait, let me check if all these primes are indeed odd. Yes, except for 2. All primes greater than 2 are odd. So yes, the intersection would be all primes less than 30 except 2. Therefore, the count is 9.

But let me make sure I didn't miss any primes. Let's list them again:

Primes less than 30:

2 (prime), 3 (prime), 4 (not prime), 5 (prime), 6 (not prime), 7 (prime), 8 (not prime), 9 (not prime), 10 (not prime), 11 (prime), 12 (not prime), 13 (prime), 14 (not prime), 15 (not prime), 16 (not prime), 17 (prime), 18 (not prime), 19 (prime), 20 (not prime), 21 (not prime), 22 (not prime), 23 (prime), 24 (not prime), 25 (not prime), 26 (not prime), 27 (not prime), 28 (not prime), 29 (prime), 30 (not prime).

So that's 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. That's 10 primes. So excluding 2, we have 9 primes that are odd. Therefore, the intersection is 9 elements.

But wait, the problem says "the set of all the prime numbers less than 30" and "the set of all the odd numbers greater than zero". The intersection is numbers that are both prime and odd. Since 2 is the only prime that's even, the rest are odd. Therefore, the answer is 9. Hmm, but let me check if there's any other even prime. No, 2 is the only one. So yes, 9 elements.

So, the final answer is 9. Therefore, the number of elements in the intersection is 9.
</think>