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For the set F = {a, b, c}, how many subsets have exactly 2 elements?

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Question: For the set F = {a, b, c}, how many subsets have exactly 2 elements?

Options:

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

Correct Answer: 3

Solution: 

The subsets with exactly 2 elements are {a, b}, {a, c}, and {b, c}. Total = 3.

For the set F = {a, b, c}, how many subsets have exactly 2 elements?

Practice Questions

Q1
For the set F = {a, b, c}, how many subsets have exactly 2 elements?
  1. 1
  2. 2
  3. 3
  4. 4

Questions & Step-by-Step Solutions

For the set F = {a, b, c}, how many subsets have exactly 2 elements?
  • Step 1: Identify the set F, which contains the elements {a, b, c}.
  • Step 2: Understand that a subset is a combination of elements from the set.
  • Step 3: We need to find subsets that contain exactly 2 elements.
  • Step 4: List all possible combinations of 2 elements from the set F.
  • Step 5: The combinations are: {a, b}, {a, c}, and {b, c}.
  • Step 6: Count the number of combinations found in Step 5.
  • Step 7: The total number of subsets with exactly 2 elements is 3.
  • Combinatorics – The question tests the understanding of combinations, specifically how to choose a subset of a certain size from a larger set.
  • Set Theory – It assesses knowledge of subsets and the properties of sets, including how to count them.
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