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

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

Options:

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

Correct Answer: 3

Solution: 

The proper subsets of D = {1, 2} are {∅}, {1}, and {2}. So, there are 3 subsets, but excluding D itself gives us 2 proper subsets.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If D = {1, 2}, what is the number of proper subsets of D?
Correct Answer: 2
  • Step 1: Understand what a subset is. A subset is a set that contains some or all elements of another set.
  • Step 2: Identify the set D. Here, D = {1, 2}.
  • Step 3: List all possible subsets of D. The subsets are: {∅} (the empty set), {1}, {2}, and {1, 2}.
  • Step 4: Count the total number of subsets. There are 4 subsets in total: {∅}, {1}, {2}, and {1, 2}.
  • Step 5: Define what a proper subset is. A proper subset is a subset that is not equal to the original set.
  • Step 6: Exclude the set D itself from the list of subsets. The set D = {1, 2} is not a proper subset.
  • Step 7: List the proper subsets of D. The proper subsets are {∅}, {1}, and {2}.
  • Step 8: Count the proper subsets. There are 3 proper subsets: {∅}, {1}, and {2}.
  • Set Theory – Understanding the definition of subsets and proper subsets, where a proper subset does not include the set itself.
  • Counting Principles – Applying combinatorial principles to count the number of subsets of a set.
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