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How many subsets of the set H = {x, y} are there that do not contain the element

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Question: How many subsets of the set H = {x, y} are there that do not contain the element y?

Options:

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Correct Answer: 1

Solution: 

The only subset that does not contain y is {∅} and {x}. Total = 2.

How many subsets of the set H = {x, y} are there that do not contain the element

Practice Questions

Q1
How many subsets of the set H = {x, y} are there that do not contain the element y?
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Questions & Step-by-Step Solutions

How many subsets of the set H = {x, y} are there that do not contain the element y?
  • Step 1: Identify the set H, which is {x, y}.
  • Step 2: Determine which subsets of H do not include the element y.
  • Step 3: List the possible subsets of H: {∅}, {x}, {y}, and {x, y}.
  • Step 4: Remove any subsets that contain y. The remaining subsets are {∅} and {x}.
  • Step 5: Count the remaining subsets. There are 2 subsets: {∅} and {x}.
  • Subsets – A subset is a set formed from another set by including some or all of its elements. The empty set is also considered a subset.
  • Set Theory – Understanding the basic principles of set theory, including how to count subsets and the significance of elements within a set.
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