Number of subsets of A which contain element 2 but not 4

To find the number of subsets of set A that contain element 2 but not 4, we need to consider that the set A has 5 elements: {1, 2, 3, 4, 5}.

Step 1: Count the total number of subsets of A.
Since A has 5 elements, the total number of subsets of A can be calculated using the formula 2^n, where n is the number of elements in the set.
In this case, n = 5, so the total number of subsets of A is 2^5 = 32.

Step 2: Count the number of subsets that contain both 2 and 4.
To count the number of subsets that contain both 2 and 4, we treat these two elements as a single entity. So, we have 4 remaining elements to consider: {1, 3, 5}.
Using the same formula as before, the total number of subsets that contain both 2 and 4 is 2^4 = 16.

Step 3: Count the number of subsets that contain only 2 and not 4.
To count the number of subsets that contain only 2 and not 4, we need to subtract the subsets that contain both 2 and 4 from the total number of subsets.
So, the number of subsets that contain only 2 and not 4 is 32 - 16 = 16.

Step 4: Finalize the answer.
The question asks for the number of subsets that contain element 2 but not 4. From Step 3, we know that there are 16 subsets that contain only 2 and not 4. However, we need to consider that the empty set is also a subset of A that satisfies this condition. So, we add 1 to the count, making it a total of 16 + 1 = 17 subsets.

Therefore, the correct answer is option D: 8.