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

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

Options:

Correct Answer: 7

Solution:

The total number of subsets is 2^3 = 8. Subtracting the empty set gives 8 - 1 = 7.

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.

Subsets – A subset is a set that contains some or all elements of another set. The total number of subsets of a set with n elements is given by 2^n.
Empty Set – The empty set is a subset that contains no elements. It is important to consider when calculating the number of non-empty subsets.