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

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

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.

Steps: 9

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}.