3. How many subsets of {a, b, c, d, e, f, h, i} are there? Show how you determined it.

1. Break Down the Problem

To find the number of subsets of a set, we need to determine the size of the set and use a mathematical formula involving powers of 2.

2. Relevant Concepts

For a set with $n$ elements, the total number of subsets is given by the formula: $\text{Number of subsets} = 2^n$ where $n$ is the number of elements in the set.

3. Analysis and Detail

In this case, the set is $\{a, b, c, d, e, f, h, i\}$ which contains 8 elements. Therefore, we can substitute $n = 8$ into our formula.

Calculating the number of subsets: $\text{Number of subsets} = 2^8$ Calculating $2^8$: $2^8 = 256$

4. Verify and Summarize

We have verified our calculation, and the number of subsets of the given set is indeed $256$.

Final Answer

There are 256 subsets of the set $\{a, b, c, d, e, f, h, i\}$.