If F = {1, 2, 3, 4}, what is the number of proper subsets of F?
Practice Questions
1 question
Q1
If F = {1, 2, 3, 4}, what is the number of proper subsets of F?
4
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15
16
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.
Questions & Step-by-step Solutions
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Q
Q: If F = {1, 2, 3, 4}, what is the number of proper subsets of F?
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.
Steps: 7
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.
