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

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

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Correct Answer: 8

Solution:

The total number of subsets of a set with n elements is 2^n. For F, n = 4, so there are 2^4 = 16 subsets. Proper subsets are total subsets minus the set itself, so 16 - 1 = 15.

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

Practice Questions

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

Questions & Step-by-Step Solutions

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

Step 1: Identify the set F, which is {1, 2, 3, 4}.
Step 2: Count the number of elements in the set F. There are 4 elements.
Step 3: Use the formula for the total number of subsets, which is 2^n, where n is the number of elements. Here, n = 4.
Step 4: Calculate 2^4, which equals 16. This means there are 16 total subsets of F.
Step 5: Understand that a proper subset is any subset that is not the entire set itself.
Step 6: To find the number of proper subsets, subtract 1 from the total number of subsets (to exclude the set F itself).
Step 7: Calculate 16 - 1, which equals 15. Therefore, there are 15 proper subsets of F.

Subsets – A subset is a set formed from the elements of another set, including the empty set and the set itself.
Proper Subsets – A proper subset is a subset that does not include all the elements of the original set, meaning it must have fewer elements than the original set.
Counting Subsets – The total number of subsets of a set with n elements is calculated using the formula 2^n.

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

What’s inside this PDF?

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

Practice Questions

Questions & Step-by-Step Solutions

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