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If F = {x, y}, how many subsets of F are there that do not contain 'y'?

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Question: If F = {x, y}, how many subsets of F are there that do not contain \'y\'?

Options:

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Correct Answer: 1

Solution: 

The subsets of F that do not contain \'y\' are {∅, {x}}, totaling 2 subsets.

If F = {x, y}, how many subsets of F are there that do not contain 'y'?

Practice Questions

Q1
If F = {x, y}, how many subsets of F are there that do not contain 'y'?
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Questions & Step-by-Step Solutions

If F = {x, y}, how many subsets of F are there that do not contain 'y'?
  • Step 1: Identify the set F, which is {x, y}.
  • Step 2: Determine which elements we want to include in our subsets. We want subsets that do not contain 'y'.
  • Step 3: The only element we can use is 'x' since we are excluding 'y'.
  • Step 4: List the possible subsets. The empty set (∅) is always a subset, and we can also have the subset that includes 'x', which is {x}.
  • Step 5: Count the subsets we have listed: ∅ and {x}. This gives us a total of 2 subsets.
  • Subsets – Understanding how to form subsets from a given set and the concept of excluding certain elements.
  • Set Theory – Basic principles of set theory, including the definition of subsets and the empty set.
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