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

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.