Questions: List all the elements of the following set. Use set notation and the listing method to describe the set. 2,4,8, ..., 256^? The complete list is (Use a comma to separate answers as needed. Use ascending order.)

Solution Steps

To list all the elements of the given set, we need to identify the pattern or rule that generates the elements. The set appears to be a sequence of powers of 2, starting from \(2^1\) and continuing until \(2^8\). We will generate these powers of 2 and list them in ascending order.

The set \(\{2, 4, 8, \ldots, 256\}\) follows a pattern where each element is a power of 2. Specifically, the elements are \(2^1, 2^2, 2^3, \ldots, 2^8\).

By calculating each power of 2 from \(2^1\) to \(2^8\), we obtain the elements of the set:

• \(2^1 = 2\)
• \(2^2 = 4\)
• \(2^3 = 8\)
• \(2^4 = 16\)
• \(2^5 = 32\)
• \(2^6 = 64\)
• \(2^7 = 128\)
• \(2^8 = 256\)

The complete set in set notation is: \[ \{2, 4, 8, 16, 32, 64, 128, 256\} \]

Final Answer