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If G = {1, 2, 3}, how many subsets of G have exactly 2 elements?

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Question: If G = {1, 2, 3}, how many subsets of G have exactly 2 elements?

Options:

  1. 3
  2. 4
  3. 5
  4. 6

Correct Answer: 5

Solution: 

The subsets with exactly 2 elements are {1, 2}, {1, 3}, and {2, 3}. So, there are 3 such subsets.

If G = {1, 2, 3}, how many subsets of G have exactly 2 elements?

Practice Questions

Q1
If G = {1, 2, 3}, how many subsets of G have exactly 2 elements?
  1. 3
  2. 4
  3. 5
  4. 6

Questions & Step-by-Step Solutions

If G = {1, 2, 3}, how many subsets of G have exactly 2 elements?
Correct Answer: 3
  • Step 1: Identify the set G, which is {1, 2, 3}.
  • Step 2: Understand that a subset is a smaller set that can be formed from G.
  • Step 3: We need to find subsets that have exactly 2 elements.
  • Step 4: List all possible combinations of 2 elements from the set G.
  • Step 5: The combinations are: {1, 2}, {1, 3}, and {2, 3}.
  • 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 study of counting, arrangements, and combinations of objects.
  • Subsets – A subset is a set formed from another set by selecting some or all elements.
  • Binomial Coefficient – The number of ways to choose k elements from a set of n elements, denoted as C(n, k) or nCk.
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