Question: If F = {1, 2, 3}, what is the number of elements in the power set of F?
Options:
3
4
6
8
Correct Answer: 8
Solution:
The power set of a set with n elements has 2^n elements. For F, n = 3, so the power set has 2^3 = 8 elements.
If F = {1, 2, 3}, what is the number of elements in the power set of F?
Practice Questions
Q1
If F = {1, 2, 3}, what is the number of elements in the power set of F?
3
4
6
8
Questions & Step-by-Step Solutions
If F = {1, 2, 3}, what is the number of elements in the power set of F?
Step 1: Identify the set F. In this case, F = {1, 2, 3}.
Step 2: Count the number of elements in the set F. There are 3 elements: 1, 2, and 3.
Step 3: Use the formula for the power set. The power set of a set with n elements has 2^n elements.
Step 4: Substitute the number of elements (n = 3) into the formula. So, we calculate 2^3.
Step 5: Calculate 2^3, which equals 8.
Step 6: Conclude that the power set of F has 8 elements.
Power Set – The power set of a set is the set of all possible subsets, including the empty set and the set itself.
Exponential Growth – The number of elements in the power set grows exponentially with the number of elements in the original set, specifically as 2^n.
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