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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?
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Q1
If D = {1, 2, 3, 4}, what is the number of proper subsets of D?
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The total number of subsets is 2^4 = 16. Proper subsets exclude the set itself, so 16 - 1 = 15.
Questions & Step-by-step Solutions
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Q
Q: If D = {1, 2, 3, 4}, what is the number of proper subsets of D?
Solution:
The total number of subsets is 2^4 = 16. Proper subsets exclude the set itself, so 16 - 1 = 15.
Steps: 7
Show Steps
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.
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