If E = {a, b, c, d}, how many proper subsets does E have?

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Question: If E = {a, b, c, d}, how many proper subsets does E have?

Options:

Correct Answer: 15

Solution:

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

If E = {a, b, c, d}, how many proper subsets does E have?

If E = {a, b, c, d}, how many proper subsets does E have?

Step 1: Identify the set E, which contains the elements {a, b, c, d}.
Step 2: Count the number of elements in the set E. There are 4 elements (a, b, c, d).
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 E.
Step 5: Understand that proper subsets are all subsets except the set itself. So, we need to exclude the set E from the total subsets.
Step 6: Subtract 1 from the total number of subsets to find the number of proper subsets: 16 - 1 = 15.
Step 7: Conclude that the number of proper subsets of E 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 element but not all elements of the original set. It excludes the set itself.