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

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

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 is the total number of subsets of D.
Step 5: Understand that proper subsets are all subsets except the set itself.
Step 6: Subtract 1 from the total number of subsets to exclude the set D itself. So, 16 - 1 equals 15.
Step 7: Conclude that the number of proper subsets of D is 15.

Subsets – A subset is a set that contains some or all 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.