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If D = {a, b}, how many subsets of D contain the element 'a'?

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Question: If D = {a, b}, how many subsets of D contain the element \'a\'?

Options:

  1. 1
  2. 2
  3. 3
  4. 4

Correct Answer: 3

Solution: 

The subsets containing \'a\' are {a}, {a, b}, so there are 2 subsets.

If D = {a, b}, how many subsets of D contain the element 'a'?

Practice Questions

Q1
If D = {a, b}, how many subsets of D contain the element 'a'?
  1. 1
  2. 2
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Questions & Step-by-Step Solutions

If D = {a, b}, how many subsets of D contain the element 'a'?
  • Step 1: Identify the set D, which is {a, b}.
  • Step 2: Understand that a subset is a combination of elements from the set D.
  • Step 3: We want to find subsets that must include the element 'a'.
  • Step 4: List the possible subsets that include 'a':
  • Step 5: The first subset is just {a}.
  • Step 6: The second subset is {a, b}, which includes both elements.
  • Step 7: Count the subsets that include 'a'. We found 2 subsets: {a} and {a, b}.
  • Step 8: Conclude that there are 2 subsets of D that contain the element 'a'.
  • Subsets – A subset is a set formed from another set by including some or all of its elements.
  • Counting Subsets – Understanding how to count subsets that include specific elements.
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