If H = {x, y, z}, how many subsets of H have at least one element?

If H = {x, y, z}, how many subsets of H have at least one element?

Step 1: Identify the set H, which contains the elements {x, y, z}.
Step 2: Count the number of elements in the set H. There are 3 elements: x, y, and z.
Step 3: Use the formula for the total number of subsets, which is 2 raised to the power of the number of elements. Here, it is 2^3.
Step 4: Calculate 2^3, which equals 8. This means there are 8 total subsets of H.
Step 5: Recognize that one of these subsets is the empty set, which has no elements.
Step 6: To find the number of subsets that have at least one element, subtract the empty set from the total number of subsets: 8 - 1.
Step 7: Calculate 8 - 1, which equals 7. Therefore, there are 7 subsets of H that have at least one element.

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