What is the number of proper subsets of the set E = {a, b}?

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Question: What is the number of proper subsets of the set E = {a, b}?

Options:

Correct Answer: 3

Solution:

The total number of subsets is 2^n = 2^2 = 4. Proper subsets exclude the set itself, so there are 4 - 1 = 3 proper subsets.

What is the number of proper subsets of the set E = {a, b}?

What is the number of proper subsets of the set E = {a, b}?

Step 1: Identify the set E. In this case, E = {a, b}.
Step 2: Count the number of elements in the set E. There are 2 elements: a and b.
Step 3: Use the formula for the total number of subsets, which is 2^n, where n is the number of elements in the set. Here, n = 2.
Step 4: Calculate the total number of subsets: 2^2 = 4.
Step 5: Understand that proper subsets are all subsets except the set itself. So, we need to exclude the full set E from our count.
Step 6: Subtract 1 from the total number of subsets to find the number of proper subsets: 4 - 1 = 3.
Step 7: Conclude that the number of proper subsets of the set E = {a, b} is 3.

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