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If C = {1, 2}, what is the number of proper subsets of C?

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Question: If C = {1, 2}, what is the number of proper subsets of C?

Options:

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

Correct Answer: 3

Solution: 

The proper subsets of a set exclude the set itself. For C = {1, 2}, the proper subsets are {∅}, {1}, and {2}, totaling 3 subsets.

If C = {1, 2}, what is the number of proper subsets of C?

Practice Questions

Q1
If C = {1, 2}, what is the number of proper subsets of C?
  1. 1
  2. 2
  3. 3
  4. 4

Questions & Step-by-Step Solutions

If C = {1, 2}, what is the number of proper subsets of C?
Correct Answer: 3
  • Step 1: Understand what a set is. A set is a collection of distinct objects. In this case, C = {1, 2}.
  • Step 2: Know what a subset is. A subset is a set that contains some or all elements of another set.
  • Step 3: Identify the total number of subsets for a set with n elements. The formula is 2^n. Here, n = 2 (since C has 2 elements).
  • Step 4: Calculate the total number of subsets. For C, it is 2^2 = 4.
  • Step 5: List all subsets of C. The subsets are: {∅} (the empty set), {1}, {2}, and {1, 2}.
  • Step 6: Define what a proper subset is. A proper subset is a subset that is not equal to the original set.
  • Step 7: Exclude the original set from the list of subsets. The original set {1, 2} is not a proper subset.
  • Step 8: Identify the proper subsets. The proper subsets of C are {∅}, {1}, and {2}.
  • Step 9: Count the proper subsets. There are 3 proper subsets: {∅}, {1}, and {2}.
  • Proper Subsets – A proper subset of a set is a subset that does not include the set itself.
  • Counting Subsets – Understanding how to count the number of subsets, including proper subsets, of a given set.
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