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

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

Options:

Correct Answer: 15

Solution:

The total number of subsets is 2^4 = 16. Proper subsets exclude the set itself, so there are 16 - 1 = 15 proper subsets.

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

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

Step 1: Identify the set C, which is {1, 2, 3, 4}.
Step 2: Count the number of elements in set C. There are 4 elements.
Step 3: Use the formula for the total number of subsets, which is 2 raised to the power of the number of elements. Here, it is 2^4.
Step 4: Calculate 2^4, which equals 16. This means there are 16 total subsets of C.
Step 5: Understand that proper subsets are all subsets except the set itself.
Step 6: Subtract 1 from the total number of subsets to find the number of proper subsets. So, 16 - 1 = 15.
Step 7: Conclude that the number of proper subsets of C is 15.

Subsets – A subset is a set formed from the elements of another set. The total number of subsets of a set with n elements is 2^n.
Proper Subsets – A proper subset is a subset that contains at least one fewer element than the original set, meaning it cannot be equal to the original set.