Final answer:
The intersection B ∩ C of the set B (all prime numbers) and set C (given as {3, 5, 9, 12, 15, 16}) is {3, 5} because 3 and 5 are the only elements in set C that are also prime numbers.
Step-by-step explanation:
The student has asked to find B ∩ C, where set B is defined as the set of all prime numbers, and set C has been provided as {3, 5, 9, 12, 15, 16}. Since prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves, we can identify which elements of set C are prime.
Out of the elements listed in set C, 3 and 5 are the only prime numbers. Therefore, B ∩ C = {3, 5}.
Note that although 2 is a prime number, it is not listed in set C, so it is not part of the intersection. Numbers like 9, 12, 15, and 16 are not prime because they have divisors other than 1 and themselves.
The intersection of two sets, B and C, denoted as B ∩ C, is the set containing all elements that are common to both sets.
In this case, B = {2, 3, 5, 7, 11, 13, 17, 19, ...} (prime numbers) and C = {3, 5, 9, 12, 15, 16}.
The intersection of B and C is B ∩ C = {3, 5}.