If D = {1, 2, 3, 4}, how many proper subsets does D have?

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Question: If D = {1, 2, 3, 4}, how many proper subsets does D have?

Options:

Correct Answer: 8

Solution:

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

If D = {1, 2, 3, 4}, how many proper subsets does D have?

If D = {1, 2, 3, 4}, how many proper subsets does D have?

Step 1: Identify the set D, which is {1, 2, 3, 4}.
Step 2: Count the number of elements in the set D. 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 D.
Step 5: Understand that proper subsets are all subsets except the set itself.
Step 6: Since there is 1 subset that is the set D itself, subtract 1 from the total number of subsets: 16 - 1.
Step 7: Calculate 16 - 1, which equals 15. Therefore, there are 15 proper subsets of D.

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 is not equal to the original set, meaning it contains at least one fewer element.