Final answer:
To find the number of subsets of the set {1, 2, 3, ..., 12} that contain exactly one or two prime numbers, you can choose one or two prime numbers and combine them with subsets of non-prime numbers. The total number of subsets is 256.
Step-by-step explanation:
To find the number of subsets of the set {1, 2, 3, ..., 12} that contain exactly one or two prime numbers, you need to identify the prime numbers in the set.
The prime numbers in the set are 2, 3, 5, 7, 11.
There are 5 prime numbers in total. Now we need to count the number of subsets that contain exactly one prime number or two prime numbers.
To do this, we can choose one prime number from the 5 and combine it with any subset of the remaining non-prime numbers.
We can also choose two prime numbers from the 5 and combine them with any subset of the remaining non-prime numbers.
For each choice, we can calculate the number of subsets using the formula 2^n, where n is the number of non-prime numbers.
Finally, we sum up the number of subsets for each choice to get the total number of subsets that contain exactly one or two prime numbers.
In this case, the total number of subsets is 2^7 + 2^7 = 256. So, there are 256 subsets of the set {1, 2, 3, ..., 12} that contain exactly one or two prime numbers.